Physics Notes Motion
Definitions and Equations:
1. Distance
2. Displacement
3. Speed
4. Velocity
5. Acceleration
Graphical Analysis:
Demo: Hydrogen Rocket Blast Off: Sketch the following graphs based on the motion of the rocket.
a. Let x = 0 and y = 0 be the location of the rocket when t = 0.
b. Let t = 0 be a moment shortly after the rocket leaves the launcher and is no longer being pushed.
c. Let up and to the right be the positive directions on the y and x axes, respectively.
x y
ax ay
Use the equations and definitions from above to answer the questions about the following graphs:
(1) x (meters)
5
0 10 t (seconds)
(a) Determine the velocity for the object over the 10 second interval.
(2)
x (meters)
5
0 3 5 t (seconds)
(a) What is the velocity of the object from: (i) 0 seconds to 3 seconds?
(ii) 3 seconds to 5 seconds?
(iii) 0 seconds to 5 seconds?
(b) What is the velocity of the object at: (i) 2 seconds
(ii) 4 seconds
(3)
x (meters)
6
4
0 2 3 4 t (seconds)
During what time intervals is:
(i) the velocity +, -, or 0?
(ii) the speed the greatest?
(iii) the velocity greatest?
Note:
(4) Determine the acceleration and the displacement of the object for each of the following two graphs: Note that the axis label has changed!
v (m/s)
5
0 10 t (seconds)
v (m/s)
5
0 10 t (seconds)
(5) Mark the location on the graph below where you will find the greatest: (a) velocity
(b) acceleration
x (meters)
0 t (seconds)
Note:
The slope of an v verses t graph is the acceleration.
Note:
Demonstration: Cart rolling down an incline
1. As the cart rolls down the incline: a. Is it stationary?
b. Is the velocity constant? c. Is it accelerating?
d. Which of the following graphs of the cart’s motion best represents: i. Position vs. Time?
ii. Velocity vs. Time? iii. Acceleration vs. Time?
A B
C
Time
Kinematics: Kinematic equations are very useful in determining what happened in an event even if we were not there to see it. They are very useful for predicting and
preventing future similar events. Kinematic equations can be employed to determine how fast someone was going when they slipped off of the road.
See the equation sheet for the three equations. V0 indicates the initial velocity.
What do you think x0 represents?
When the cart rolls down the incline, what could we measure to help determine: 1. The acceleration of the cart?
2. The velocity of the cart at the end of the ramp?
As a class: Determine the acceleration of the cart.
Kinematics Practice:
1. A rock is dropped into a well and a “plop” is heard 1.75 seconds later. How far from the top of the well is the water level?
2. A cannonball is shot directly upward with a speed of 55 m/s. a. Chose a direction to be positive.
b. How high does the cannonball reach?
c. How much time does it take to reach this height?
3. A car traveling 35 m/s decelerates at a rate of 8.5 m/s2 until it reaches a stop. a. How far does the car skid?
b. How much time does it take the car to come to rest?
4. A car accelerates at a constant rate from 30 m/s to 40 m/s while it travels 60 meters. How long does it take to achieve this speed?
Note:
For a freefalling body, a = 9.8 m/s2 down.
Note:
Vector and Scalar Quantities:
Vector: Quantity that has a direction. (Example: velocity (56 m/s or – 3.4 m/s)
Scalar: Quantity that does not have a direction. (Example: 30 mph, 18 m/s)
Resultant Vector: The vector created by the combination of two or more vectors.
Resultant Vectors:
1. Logic: Let’s say that you go out to the airport and walk on the moving sidewalk. The sidewalk is moving to the left at 2 m/s.
a. You decide to walk to the left on the moving sidewalk. You move 3 m/s compared to the moving sidewalk. How fast will you be going compared to the people standing on the airport floor?
b. You then turn around and walk at the same speed to the right. How fast will you be going compared to the people standing on the airport floor?
c. Draw vectors for each of the above.
d. How do head winds and tail winds affect travel time for airplanes?
2. Example Problems:
b. Repeat the previous problem, but change the wind to a tail wind.
c. As a class: A toy airplane flies west with an air velocity of 4 m/s. While flying it experiences a cross-wind of 3 m/s moving due north.
i. Draw a vector diagram of this problem.
ii. Determine the following for the resultant vector: 1. Magnitude
2. Direction (angle)
hypotenuse opposite
Θ
adjacent
d. Individual Practice: Determine the magnitude and direction of the resultant vector of 10 m/s north and 15 m/s east.
North
10 m/s
15 m/s
East Math Notes:
a2 + b2 = c2
Sin Θ = opposite/hypotenuse
Cos Θ = adjacent/hypotenuse
Component Vectors:
Equilibrant Vector: The vector required to cause equilibrium.
Component Vector: The vectors that make up a resultant vector.
1. Class Problem: For the vector below, what are the north and west component vectors?
N 50 m/s
40° W
2. Practice:
a. A football is kicked to a velocity of 23 m/s at 65° above the horizontal. At what speed on the ground will the shadow of the football travel?
23 m/s
65°
b. An airplane travels 550 m/s 12° east of north. How fast is it traveling in the northward direction?
N 550 m/s
12°
Projectile Notes:
1. A projectile is fired with an initial velocity of 20 m/s at an angle of 25° with the horizontal and follows the trajectory shown below. Assume negligible air resistance. Points A and C are the same distance from the ground.
B
20 m/s A C
25°
a. How do the speeds of the projectile compare at Positions A, B, and C?
b. What are the projectile’s initial horizontal and vertical speeds?
c. What happens to the vertical and horizontal speeds as the projectile moves through the air?
d. Sketch rough graphs of both the horizontal and vertical velocities of the projectile as a function of time. (Let up and right be positive.)
Horizontal Velocity Vertical Velocity
time time
Starters:
e. What causes the acceleration of the projectile and in what direction?
f. Sketch rough graphs of both the horizontal and vertical accelerations of the projectile as a function of time. (Let up and right be positive.)
Horizontal Acceleration Vertical Acceleration
time time
g. How much time will the projectile spend in the air?
Practice: Assume negligible air resistance.
1. A rock is thrown horizontally from the top of a 45 meter tall building with an initial speed of 16 m/s.
a. Sketch a diagram of the rock’s trajectory.
b. Determine the following for the x-axis and the y-axis:
x Axis y Axis
Initial Velocity Acceleration
c. Calculate the amount of time elapsed from launch until hitting the ground. (Hint: Which axis (x or y) determines the time until it hits the ground?)
