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~ 25% of the course 1 Test
4 Sub - Topics Graphing
Kinematics formulae Freefall
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Lesson 1.01 Intro to Physics
Unit 1 - Kinematics
What is physics?
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Base Units (see p. 802)
Science is about measuring stuff. We need to agree on the units we intend to use to measure. The base units of science in the metric system (SI) are: distance - __________________
mass - _____________________
time - _____________________
Derived Units
figured out from base units. ex: speed is
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Metric Prefices
M - Mega x 106 k - kilo x 103 h - hecta x 102 da - deca x 101 __
d - deci x 10-1 c - centi x 10-2 m - milli x 10-3 μ - micro x 10-6
To convert from one metric prefix into another: 1. Count the # of loops from the unit you start with. 2. Move the decimal that many places in that direction. ex: Convert 1.03 km into m
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Scientific Notation
Used for representing really large, or really small numbers.
3.00 x 104 m/s 2.4 x 10-6 s
Your calculator will probably use an “EXP” or an “EE” or a “x 10x” button to represent these numbers. You will NOT use the multiply button to represent them.
Using your calculator, find the correct response and write your answer using scientific notation. 6.2 x 10 - 6
3.1 x 10 - 3
(4.8 x 10 – 3) (3.7 x 10 5) 1.8 x 10 - 6
Significant Digits
Those digits that carry meaning contributing to the _______________________of a measurement.
Precision: a measure of _______________________________________________________, generally determined by the device you are using.
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Determining the number of significant digits
All ________________________ are significant. Ex: 235 has 3 significant digits.Zeros are wacky.
1. Leading zeros (in front) __________________________ count. Ex:
2. Middle zeros _____________________________ count.
Ex:
3. Trailing zeros ______________________ count. Ex:
Calculation with Significant Digits
When you multiply or divide, you round your answer to the lowest number of significant digits. ex: 1.07 x 0.38 =
When you add or subtract, you round your answer to the least number of decimalplaces.
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Algebraic rearrangement of equations
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Practice Set
Unit Conversions and Intro material Write the following in scientific notation:
1. 156.90 _________________ 3. 0.0345 _________________ 2. 12 000 _________________ 4. 0.000890 _______________ Expand the following numbers:
5. 1.23 x 106 _________________ 7. 1.54 x 104 _______________
6. 2.5 x 10-3 _________________ 8. 5.67 x 10-1 _______________
Solve the following and leave your answer in scientific notation:
9. 6.6 x 10-8 = ________________ 11. (1.56 x 10-7) x (2.43 x 10-8)_________________
3.3 x 10-4
10. 7.4 x 1010 = ________________ 12. (2.5 x 10-6) x (3.0 x 10-7) _________________
3.7 x 103
Give the number of significant digits in each of the following measurements: 13. 2.9910 m___________ 15. 0.00670 kg ___________
14. 5600 km ___________ 16. 809 g ___________
Solve for x in the following problems
17. 3x = 6g 19. 2x2 = dg
y B 3
18. d = t 20. 2√x = y
x c
Convert the following
21. 4008 g = mg 24. 2.0 x 106 μs = s
22. 48 mL = L 25. 1.4 cg = mg 23. 239 km = m 26. 2.3 x 103 m = Mm
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Answers to Practice Set 1. 1.569 x 102
2. 1.2 x 104
3. 3.45 x 10-2
4. 8.9 x 10-4
5. 123 0000 6. 0.0025 7. 15400 8. 0.567 9. 2.0 x 10-4
10. 2.0 x 107
11. 3.79 x 10-15
12. 7.5 x 10-13
13. 5 14. 2 15. 3 16. 3
17. x = 2gy / B 18. x = t / d 19. x = √(3dg/2) 20. x = c2y2
4 21. 4008000 mg 22. 0.048 L 23. 239 000 m 24. 2.0 s 25. 14 mg 26. 2.3 x 10-3 Mm
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Warmup:
Convert the following: 250 kL into daL 1.5 MF into kF
1.4 x 104 m into standard form 0.000 86 s into scientific form
Compute and leave your answer in scientific notation: 1.4 x 106
3.2 x 10 - 2
Lesson 1.02 Kinematics
Unit 1 – Kinematics
A branch of ________________________ (the study of how and why objects move).
Kinematics seeks to ____________________________________________________, without studying the cause of motion, we will leave that to unit 2.
* grab a text book
* refer to duck diagram on p.3
Process of kinematics: ⇨ Observe event
⇨ Measure and record data
⇨ Analyze data by Graph and calculation ⇨ Generate theories and equations
Vectors and Scalars
Vectors have a ________________________ (size), _______________ and ________________ Ex: 10 km/hr [North]
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(Vectors always have an arrow over the symbol)
Scalars have a magnitude and unit, but ___________________________________ Ex: 10 km/hr.
Drawing Vectors
Directions for vectors are always given in _____________________________________. Example : 10.0 m [E55°N]
Distance/Displacement
Distance, d - measure of total travel. ______________________________ (m)
Displacement, 𝑑⃑ - measure of net travel from start to finish. _______________________ (m)
Vectors are added ______________________________ and the net or resultant vector is drawn _____________________________________________________________________________.
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ex: You drive north for 50.0 km and then South for 30.0 km a) What is your total distance, d
b) What is your total displacement, 𝑑⃑
ex: You drive north for 50.0 km and then East for 30.0 km a) What is your total distance, d
b) What is your total displacement, 𝑑⃑⃑⃑⃑
1. Find Magnitude from Pythagoras
2. Find the angle from trig. SOH CAH TOA
*notice that we could have gotten the same answer had we drawn the other vector first.
Vectors are added “tip-to-tail” and the net or resultant vector is drawn
from the start point to the tip of the last arrow drawn.
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Ex 2: For the following three vectors; a) Draw the resultant vector (add tip to tail) b) Calculate the total distance travelled c) Calculate the net displacement
d1 = 4.3 m [N] d2 = 5.2 m [N] d3 = 7.4 m [W]
Speed/Velocity
Speed
: Distance divided by time.(m/s) May be _________________ (total distance) or______________________________. (speed at a particular time) ____________
Velocity
: Displacement divided by time. (m/s) May be _________________ (totaldisplacement) or ______________________ (velocity at a particular time) ________________
(Note that the _______________________ of a velocity vector is always the same as the ___________________________________ vector that you used to obtain it.)
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ex: You move 5.00 m [E], then 3.00 m [E], then 6.00 m [S] in 8.00 s.
Find: d, 𝑑⃑, v, 𝑣⃑,
The meaning of "delta" Δ
Unit analysis
How many minutes are in a year?
Convert 1 km/hr into m/s
rulers next day...we’ll be graphing some motion.
Homework: Read: p 2-12, pay attention to the borders, which have useful information Assign Practice Set – Vectors
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Practice Set Vectors
1. Draw the resultant vector for the sets of vectors below. (Remember that resultant or net vectors go from the beginning to the end and are usually drawn with a dashed line)
2. Sketch each of the following vectors:
Vector Diagram
10.0 m [E]
25.0 m [W]
12.0 m/s [E45°N]
22 m [S30°E]
15.0 m/s/s [up]
2.0 m [S30°E]
1.5 m [E40°S]
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Remember:
Speed is calculated using distance
Velocity is calculated using displacement
The direction of the velocity vector must be the same as the displacement vector.
3. For each of the following problems complete the table. i) Draw a vector diagram
ii) Draw the resultant vector (dashed line) iii) Calculate the distance traveled
iv) Calculate the net displacement v) Calculate the average speed vi) Calculate the average velocity
a) You move 3.0 m [E] followed by 5.0 m [E] in 45 seconds. b) You move 2.0 m [E] followed by 5.0 m [W] in 45 seconds. c) You move 3.0 m [W] followed by 5.0 m [S] in 45 seconds. d) You move 4.0 m [S] followed by 6.0 m [E] in 45 seconds.
Vector Diagram (Include Resultant Vector) Total Distance (m) Total Displacement (m) Average Speed (m/s) Average Velocity (m/s) a) b) c) d)
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1.03 Graphical Representation
Displacement - time graphs (also called position time graphs) (see p.14) represent an object's ___________________________________ over time.
Uniform Motion
Motion at a constant speed in a straight line. A straight line d-t graph.
Uses of a graph in physics
1. Read the graph: tells you what is on the_____________. Reading a d-t graph tells you __________________________ position (m)
2. Get slope: slope of a d-t graph tells you instantaneous _________________ (m/s) 3. Get area: area under a d-t graph tells us ________________ (for a d-t graph)
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1. Describe the motion of the object (words)
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Example 2
Describe the motion of the object (words)
2. Create a v-t graph from the d-t graph (slope of each section)
Read p. 12-19
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d( m )
t( s) 15
- 15
5 10
d( m )
t( s) 10 15
- 15
d(m)
t(s) 5 3
-3
Practice Set -
Graphing Uniform Motion 1.)a) What is the velocity of the object at 10 s?
b) When is the object stopped?
2.) a) Describe the motion of the object.
b) What is the position of the object at 6.0 s?
3.) a) What is the velocity of the object at t = 1.0 s?
Page 21 of 54 d(m) t(s) 10 6.0 -6.0 0
d( m )
t( s)
5 10
15
- 15
d( c m ) t( s)
2 6
15
- 15
4
d( km )
t( hr )
0.5 1.0
12 0
- 120
4.) a) What is the velocity of the object at t = 8.0 s?
b) Describe the motion of the object.
c) What is the speed of the object at t = 8.0 s?
5.) a) What is the velocity of the object at t = 1.0 s?
b) What is the instantaneous position of the object at 5.0 s?
6.) a) What is the velocity of the object at t = 5.0 s?
b) Describe the motion of the object.
c) What is the average velocity of the object between 2.0 and 6.0 s?
7.) a) What is the velocity of the object at t = 0.6 hr?
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1.04 Analysis of Curved d-t graphs
To get the slope for a curved line we must use a ________________________ (A straight line touching the curve at only one point)
Refer to p. 21 for complete tangent line instructions. a) Choose a _______________________
b) Draw a straight line touching only once c) calculate _____________________
Notice that the units of rise/run still gives us m/s, so slope is still a velocity, however, since slope changes, velocity changes.
Thus, what we find from a tangent line is ___________________________ velocity, and since the velocity ____________________________, the object is ____________________________.
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Which way is it moving?
__________________ __________________ __________________ ____________________
How do we know?
__________________ __________________ __________________ ____________________
Speeding up or slowing down?
__________________ __________________ __________________ ____________________
How do we know?
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Practice Set - Algebra
“You know nothing until you have practiced it” R. Feynman
1. Rearrange the following equations for x.
Equation Rearranged
a y = mx + b
b x2 - 4c = 17 c x2 - 4b = 17
3
d 3x2 = 2 4y
e √(x2 - y2) = 0 f √x = y + 3
g √(x - y) = 2
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2. Solve each equation below for the unknown variable. Grayed out variables are to be omitted. For example, in (a) there is no way to solve for vf
Equation: vi Δt a d vf
a d = viΔt + ½ a Δt2 - 12.0 1.20 -9.80 ?
b 2ad = vf2 - vi2 ? 19.9 - 42.5 - 8.75
c vf = vi + aΔt 0 1.2 ? 12
d d = vfΔt - ½ a Δt2 4.53 ? 221 27.8
e d = ½ (vi + vf) Δt ? 1.34 13.2 1.98
f d = viΔt + ½ a Δt2 ? 2.33 1.23 13.2
g 2ad = vf2 - vi2 1.23 ? -7.85 -2.23
h vf = vi + aΔt 11.0 ? -1.37 1.24
Solutions:
Rearranged Solved
1a x = (y - b) m
2a -21.5
1b x = √(17 + 4c) 2b 42.0
1c x = √(51+ 4b) 2c 10.0
1d x = √(8y/3) 2d -9.27
1e x = y 2e 17.7
1f x = (y + 3)2 2f 4.29
1g x = y + 4 2g -0.220
1h x = √(8/y) 2h 7.12
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Which way is it moving?
__________________ __________________ __________________ ____________________
How do we know?
__________________ __________________ __________________ ____________________
Speeding up or slowing down?
__________________ __________________ __________________ ____________________
How do we know?
__________________ __________________ __________________ ____________________
Which way is it moving?
__________________ __________________ __________________ ____________________
How do we know?
__________________ __________________ __________________ ____________________
Speeding up or slowing down?
__________________ __________________ __________________ ____________________
How do we know?
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d( m )
t( s) 15
- 15
d
t
d d d
t t
t
A B C D
d
t
d v d
t t
t
A B C D
d(cm)
t(s)
5 10
6.0
0
Practice Set - Motion Graphs
1. For the graph below calculate the instantaneous velocity at the labeled points A and D
2. Describe the motion in each graph.
3. Match each graph below with the appropriate description. More than one graph may fit each description.
a. Object is stopped _____ b. Object moving left _____ c. Object moving right _____
d. Object moving with uniform motion __________ 4. Use the d-t graph below to answer the questions which follow.
a) What is the object’s position at 2.0 s? _____ b) What is the object’s velocity at 2.0 s? _____ c) What is the object’s velocity at 8.0 s? _____ d) What is the average velocity between 0 and
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t( s)
5 10
6.0
- 6.0 0
v( c m /s)
t( s) 5 10 3.0 - 3.0 v(cm/s) t(s) 5 10 3.0 -3.0 v t (s) 10 (m /s) 0
8
5. Use the d-t graph below to construct a v-t graph.
6. Use the v-t graph below to answer the questions which follow. a. What is the object’s velocity at 2.0 s? _____
b. What is the object’s velocity at 10.0 s? _____
c. How far has the object traveled in the first 6.0 s? _____
d. Describe the motion of the object. ______________________________________ __________________________________________________________________ e. Does the object go farther to the right or to the left? How do you
know?____________________________________________________________
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i) What is the velocity of the object at 1.0 s? _______ ii) What is the acceleration of the object at 2.0 s? ______
iii) What is the displacement of the object for the period t = 0.0 s to t = 10.0 s? _____ iv) What is the distance traveled for the period t = 0.0 s to t = 10.0 s? _____
v) What is the average velocity for the trip? ______ vi) What is the average speed for the trip? ______
8. Sketch the graphs in the space provided
Uniform motion
d-t graph v-t graph
i) moving left
ii) moving right
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Uniform acceleration
d-t graph v-t graph
iv) moving left speeding up
iv) moving right slowing down
vi) moving left slowing down
vii) moving right speeding up
1a 3.94 m/s 4i 1.33 cm 7i 4.00 m/s 8v p. 47
1d - 4.50 m/s 4ii 0.670 cm/s 7ii - 4.00 m/s/s 8vi p. 47
2i moving right uniform motion 4iii 0 7iii -22.0m 8vii p. 47
2ii moving right uniform motion 4iv 0.333 cm/s 7iv 38.0 m
2iii stopped 5 see notes 7v -2.20 m/s
2iv moving left uniform motion 6i 2.00 cm/s 7vi 3.80 m/s
3i B 6ii -1.00 cm/s 8i p. 47
3ii D, C 6iii 12.0 m 8ii p. 47
3iii A 6iv see notes 8iii p. 47
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What do each of these graphs tell us about motion?
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What does the point of intersection of these graphs represent?
Hwk: p.23-25 read (note summary p.25) p. 46 #1, 2
(see p. 43 for the figure) From 0 to 2.0 s and then from 0 to 7.0 s. p. 46 #4 (see p. 20 for the figure)
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Problem Solving Methodology
1. Read. Read again.
2. Picture. Mental or otherwise. 3. List givens and unknown
* Check Units! 4. Choose Equation
5. Substitute in givens (with units)
6. Solve. Check. Units? Vector? Sig digits? Reasonable?
1.08 Using Formulae
Ex 1: A Ferrari, moving at 20.0 km/hr, accelerates to 230.0 km/hr in 7.5 s. How far does it travel?
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Ex 2: A braking system brings a car to a complete stop from 25.0 m/s in 17.0 m. What is the acceleration?
p. 64 # 1 - 3 p. 73 # 33 - 43
* for #41 laser moves with speed of light, c = 3.00 x 108 m/s (uniform) for #42 circumference of circle = 2πr
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1.09 Freefall
Warmup: A rocket is moving through space at - 27.0 m/s when it begins
to accelerate at + 2.0 m/s/s for 3.0 seconds. It then continues at this speed for 4.0 seconds. a) How far in total has it traveled?
b) Sketch a d-t and v-t graph of the object's motion.
A free-falling object is an object which is falling under _________________________________. There are some important motion characteristics which are true of free-falling objects:
1. Free-falling objects _______________ encounter air resistance.
2. All free-falling objects (on Earth) accelerate downwards at a rate of ____________________ 3. An object moving *up* may still be in "freefall"
Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration.
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Freefall "CODE"
acceleration = g = - 9.80 m/s2 'dropped' or 'thrown'
'dropped' means v1 = 0
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Ex 1. Upton Chuck is riding the Giant Drop at Great America. If Upton free falls from rest for 2.6 seconds, what will be his final velocity and how far will he fall?
Ex 2: A person stands on a 4.0 m high ledge.
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b) If she instead throws it vertically with v1 = + 6.2 m/s, i) how high above the ledge will it go?
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Practice Set - Freefall
The equations of kinematics for uniform acceleration also apply to the special case of an object that is accelerating near the earth’s surface. The gravitational pull of the earth on any object will cause it to accelerate towards the centre of the earth at a rate of 9.80 m/s2, assuming air resistance is negligible. Thus, for any equations involving a body in free fall (something that is dropped or thrown) we can use the same problem solving skills we already have. There are a few unique features to solving freefall problems.
* acceleration is always constant at g = -9.80 m/s2 (the negative is very important)
* at the top of its flight, an object has v = 0. (since it must stop before starting to come down again)
* keeping your sign conventions for direction is very important...all velocity directed down must be negative, and all velocity directed up must be positive.
1. A tourist drops a rock from rest from a guard rail overlooking a valley. What is the velocity of the rock at 4.0 s? What is the displacement of the rock at 4.0 s?
2. Suppose the tourist in question #1 instead threw the rock with an initial velocity of 8.0 m/s [down]. Determine the velocity and displacement of the rock at 4.0 s (Remember the vi is down and must become a -8.0 m/s)
3. Suppose the tourist in question #1 instead threw the rock with an initial velocity of 8.0 m/s [up]. Determine the velocity and displacement of the rock at 4.0 s (Remember the vi is up and must become a +8.0 m/s)
4. A college student wants to toss a textbook to his roommate who is leaning out of a window directly above him. He throws the book upwards with an initial velocity of 8.0 m/s. The roommate catches it while it is travelling at 3.0 m/s [up].
a) How long was the book in the air? b) How far vertically did the book travel?
c) Redo the problem, and have the roommate catch the book as it is travelling 3.0 m/s [down]. What is the time and displacement now? Do you notice anything?
5. A man is standing on the edge of a 20.0 m high cliff. He throws a rock vertically with an initial velocity of 10.0 m/s.
a) How high does the rock go? (Remember that at its max height v = 0 m/s) b) How long does it take to reach its max height?
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Solutions: 1.
Given: vi = 0 m/s
a = g = -9.80 m/s2
t = 4.0 s Find: v = ?
d = ? Soln: v2 = v1 + at
v2 = 0 + (-9.80 m/s2)(4.0 s)
v2 = -39.2 m/s
d = v1t + ½ at2
d = 0 + ½ (-9.80 m/s2)(4.0 s)2
d = -78.4 m
2.
Given: vi = - 8.0 m/s
a = g = -9.80 m/s2
t = 4.0 s Find: v = ?
d = ? Soln: v2 = v1 + at
v2 = -8.0m/s + (-9.80 m/s2)(4.0 s)
v2 = -47.2 m/s
d = v1t + ½ at2
d = (-8.0m/s)(4.0s) + ½ (-9.80 m/s2)(4.0 s)2
d = -110.4 m
3.
Given: vi = + 8.0 m/s
a = g = -9.80 m/s2
t = 4.0 s Find: v = ?
d = ? Soln: v2 = v1 + at
v2 = +8.0 m/s + (-9.80 m/s2)(4.0 s)
v2 = - 31.2 m/s
d = v1t + ½ at2
d = (8.0 m/s)(4.0 s) + ½ (-9.80 m/s2)(4.0 s)2
d = -46.4 m
* this is smaller, because the object must travel up first, then down, so its net displacement is less.
4.
Given: vi = 8.0 m/s [up]
v2 = 3.0 m/s [up]
a = g = -9.80 m/s2
Find: t = ? d = ? Soln:
a)
t =0.51s
b)
d = 2.80 m
c)
Given: vi = 8.0 m/s [up]
v2 = 3.0 m/s [down]
a = g = -9.80 m/s2
Find: t = ? d = ? Soln:
t = 1.12 s
d = 2.80 m
*Notice that the time was longer, as the book went up past the roommate and was caught on the way down. The displacement was the same however...she caught it at the same net displacement.
5.
Given: vi =10 m/s
a = g = -9.80 m/s2
h = 20.0 m Find: d = ?
t = ? Soln: v2 = v1 + at
0 = 10 + (-9.80 m/s2)(t)
t = 1.02 s
d = v1t + ½ at2
d = (10.0 m/s)(1.02s) + ½ (-9.80 m/s2)(1.02s)2
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1.10 Reference Frames
Relative Motion
The motion of an object depends on where the ___________________ of the motion is located. Consider the example of two cars on the highway
Moving Reference Frames
When the ______________ is moving (the river, the air, the sidewalk in an airport) the motion of the object relative to the ground is a combination of two vectors
Velocity of the object relative to the _________________ (𝑉⃑ og)
Velocity of the moving _______________________ (𝑉⃑ mg) (usually the wind or river)
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Ex: An aircraft can fly at 100 km/hr [S] in still air. The wind is blowing at 25 km/hr. Find the velocity of the plane relative to the ground if the wind is blowing to the:
a. [South] b. [North] c. [East]
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d) What must be the plane's heading in order to fly due south if the wind is still blowing to head East?
Homework: Read p. 95-98 p. 114 #14
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Practice Set
Relative Velocity in 2 - Dimensions
There are only two options for crossing a river (or flying a plane in a wind) that deal with right triangles. You can either head straight across the current and get pushed downstream, or you can angle yourself into the current so as to arrive straight across from where you started.
1. Julia can swim at 3.5 km/hr in still water. She attempts to head straight north across a river with a current flowing at 1.2 km/hr [W]. What is her resultant velocity v og ? (3.7 km/hr [N19°W])
2. In problem #1, at what angle should Julia aim in order to land directly across the river from her start point? (must aim at [N20°E])
3. An aircraft has an airspeed of 230 km/hr [N]. What is the plane’s speed relative to the ground if it:
a) Flies with a tailwind of 50 km/hr? (280 km/hr [N]) b) Flies into a headwind of 50 km/hr? (180 km/hr [N])
c) Flies due [N] while the wind blows at 50 km/hr [E]? (235 km/hr [N12°E])
4. An aircraft leaves Albany for New York, which is due south. If the aircraft can fly at 450 km/hr, and the wind is blowing to the west at 40 km/hr, what must be the aircraft’s heading in order to fly due south? ([S5°E])
(Heading is the angle of the planes velocity relative to the ground)
(Ground speed is the magnitude of the plane’s velocity relative to the ground)
5. A navy vessel is patrolling the Straights of Hormuz for oil smugglers. The ship can travel at 30 km/hr in still water. If the current is 3.0 km/hr [W], what must be the ship’s heading to maintain a course due [N]? (head [N5.7°E])
6. A swimmer jumps into a river and swims straight for the other side at 1.5 km/hr relative to the water. There is a current in the river of 2.0 km/hr [W]. What is the swimmer’s velocity relative to the shore? (2.5 km/hr [N53°W])
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Unit Review – Kinematics
Acceleration is defined as the change in velocity divided by the change in time. It is a vector. An acceleration of +2.0 m/s/s means that each second, the velocity changes by +2.0 m/s.
If you start from rest v = 0 m/s with acceleration of +2.0 m/s2 then my velocity
after 1.0 second is _________ after 2.0 seconds is _________ after 3.0 seconds is _________ after 4.0 seconds is _________ after 5.0 seconds is _________ after 6.0 seconds is _________
1. Graph this motion
2. Is this motion uniform? How can you tell?____________________________________
3. From the graph, What is the instantaneous velocity at 1.0 s = _________________
3.0 s = _________________ 6.0 s = _________________
4. What is the slope of the line? _______________________
5. The slope of the line from a v-t graph tells me the acceleration. What is the acceleration of
this object? _______________ (don’t forget the unit)
6. Describe the motion of this object. Is it moving to the right or left? Is it speeding up or
slowing down? _________________________________________________________
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v
t (s) 6
6
(m/s)
v
t (s) 6
6
(m/s)
v
t (s) 6
6
(m/s)
8. The area under a v-t graph tells us the displacement. Calculate the displacement under each
v-t graph. Don’t forget your unit (meters)
A B C
9. The above? slope of a v-t graph means acceleration. What is the acceleration for each of the objects
a) _____________________
b) _____________________
c) _____________________
10. The initial velocity is the velocity at time zero (t = 0.0 seconds). You get this from the y-intercept of the v-t graph. What is the initial velocity for each of the objects above?
a) _____________________
b) _____________________
c) _____________________
11. How do you know if the object is speeding up or slowing down? Check to see if the velocity
becomes bigger or smaller over time. For each of the graphs above describe its motion. (Speeding up or slowing down?)
a) _____________________
b) _____________________
c) _____________________
12. How do you tell if the object is moving right or left? The velocity will tell you. Positive
velocities are to the right, negative velocities are to the left. Which way is each object
moving above? (Be very careful with B!!) Moving left? Moving right?
a) _____________________
b) _____________________
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v
t (s) 6
12
( m /s) 10 8 6 4 2 0
13. Now we can bring all our knowledge together. Graph the v-t graph for the motion given
below.
v (m/s)
t (s)
12 0
11 1
10 2
9 3
8 4
7 5
6 6
a) What is the acceleration of the object? (Slope) _________ (Unit? Sign?)
b) What is the displacement of the object from 0-6 seconds? (Area) _____________
c) What is the initial velocity of the object? (Y-intercept) __________________
d) What is the instantaneous velocity at t = 4.0 seconds? ___________________
e) Is this object speeding up or slowing down? ____________________
f) Is this object moving to the right or to the left? __________________
Solutions:
1 Graph 11 speeding up, slowing down, speeding up 2 No. Velocity is changing 12 moving right, moving right, moving right 3 2.0 m/s, 6.0 m/s, 12.0 m/s 13a -1.0 m/s2
4 2.0 13b +54 m
5 +2.0 m/s2 13c +12 m/s
6 moving right, speeding up 13d +8.0 m/s 7 displacement 13e slowing down 8 +15 m, +18 m, + 24 m 13f moving right 9 0.83 m/s2, -1.0 m/s2, 0.33 m/s2
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1. Check your notes, your text, or your table for the answers to the following.
a) If the speed of an object remains constant, can its velocity change? Explain.
b) If the velocity of an object remains constant, can its speed change? Explain.
c) Can an object have a westward velocity while experiencing an eastward acceleration?
Explain.
d) Is it possible to have zero velocity and still have acceleration? Explain.
e) Is it possible to have zero acceleration and still have velocity? Explain.
2. Sketch the following d-t and v-t graphs:
a) moving left speeding up followed by uniform motion to the left b) uniform motion to the right then slows down and stops
c) moving right slowing down, stops, then moves left and speeds up
3. A boy on a ten speed bicycle accelerates from rest to 2.2 m/s in 5.0 s in 3rd gear, then changes
into 5th gear. After 10.0 s in 5th gear he reaches 5.2 m/s. Calculate the average acceleration
in the 3rd and 5th gears.
4. How long will it take a freely falling object, starting from rest, to reach a velocity of 63.7 m/s
[down]?
5. A ball is thrown vertically upwards. What is its acceleration:
a) after it has left the thrower’s hand and is travelling upwards?
b) on the instant it reaches the top of its flight?
c) on its way down?
6. A student throws a ticker tape timer vertically upwards, and 2.8s later it returns to the height
from which she threw it. Ignoring air resistance, calculate the following:
a) The initial velocity
b) The height the timer reached.
7. An arrow is accelerated for a distance of 80.0 cm while it is on a bow. If the arrow leaves the
bow with a velocity of 80.0 m/s, what is its average acceleration while on the bow?
8. A carpenter wants to throw a 1.2 kg hammer to a height of 6.0 m so that it will land with zero
velocity on a roof. What initial vertical speed must be given to the hammer?
9. An athlete in good physical condition can land on the ground at a speed of 12 m/s without
injury. From what maximum height can an athlete safely jump?
10. An object travels 12.2 m and reaches a final velocity of 60 km/hr in 0.85 s. What was the
initial velocity?
11. A ball is dropped from a height of 15 m. With what velocity does it strike the ground?
12. Bob is on a moving walkway 200 m [W] of the terminal. If his dog is on a leash 1.0 m ahead
of him, what is the dog’s displacement relative to the terminal if they are: a) heading towards the terminal
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13. A water bug can swim at 0.1 m/s in still water. What is the bug’s speed relative to the shore
if the stream is flowing at 0.05 m/s [N] and the bug heads: a) upstream
b) downstream
14. A swimmer can swim at 5.6 km/hr in still water. If the river has a current of 2.0 km/hr [E]
and the swimmer is on the north bank, what must be the heading of the swimmer to land exactly across from where they began? If the river is 300 m across, how long will this take?
15. A boat can travel at 35 km/hr in still water. If the river’s current is 12.0 km/hr [N] and the
boat tries to head due [E], what is the resultant velocity of the boat? If the river is 800 m across, how far downstream will the boat land?
16. Car A has v of 100 km/hr [W] relative to the ground. What is the velocity of car B relative to
car A if car B is travelling: a) 100 km/hr [W] b) 100 km/hr [E]
For both the cases above, what is the velocity of car A relative to car B?
17. A speeder is moving with uniform motion at 65 km/hr when she passes a stationary cop on
the side of the road. The cop immediately begins to accelerate at 2.23 m/s/s.
a) how long does it take to catch the speeder?
b) how far has the cop travelled in this time?
18. A two stage rocket starts from rest and accelerates at 17.3 m/s/s until reaching its top speed of
263 m/s. It then travels at this speed for 4.2 seconds. How far does it travel in total?
19. An object is falling for 3.0 seconds from rest before applying a rocket brake which causes it
to slow with an acceleration of + 4.9 m/s2.
a. How far does it fall in total before stopping?
b. Sketch the d-t and v-t graph for the object’s motion.
20. A toy rocket is taking off from the ground, accelerating at + 1.2 m/s2 for 4.0 s. The fuel runs
out and the rocket continues upwards in freefall.
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1a notes 6b d= 10 m [up] 17a 16.2 s
1b notes 7 4.0 x 103 m/s2 17b 293 m
1c notes 8 11 m/s [up] 18 3100 m
1d notes 9 7.3 m 19 132.3 m
1e notes 10 12.0 m/s 20 13.04 m
2a notes 11 vf = - 17.1 m/s
2b notes 12a 199 m [W]
2c notes 12b 201 m [W]
3 0.44 m/s2, 0.30 m/s2 13a 0.05 m/s [S]
4 6.5 s 13b 0.15 m/s [N]
5a 9.80 m/s2 [down] 14 [S20.9°W], 207s
5b 9.80 m/s2 [down] 15 37 km/hr [E18.9°N], 274 m 5c 9.80 m/s2 [down] 16a 0, 200 km/hr [E]
6a v = 14 m/s [up] 16b 0, 200 km/hr [W]
This is the end of Unit 1 – Kinematics. 25% of the year is now complete. Congrats.
