Physics Lecture Notes
1.1 Linear Motion
White Station High Physics Club
Memphis, Tennessee
1.1 Linear Motion
KHAN ACADEMY Science > Physics > One-dimensional motion
Watch and read the following for a basic understanding. If you want you can watch the other videos in the section. Use 2x speed on videos if you want and/or skip things you already know.
● Intro to vectors and scalars ● What is displacement?
● Calculating average velocity or speed ● Solving for time
● Displacement from time and velocity ● What are position vs. time graphs ● Acceleration
● What is acceleration?
● Why distance is area under velocity-time graph ● What are velocity vs. time graphs
● Average velocity for constant acceleration
● Deriving displacement as a function of t, a, and 𝑣o
● Plotting projectile displacement, acceleration, and velocity ● Impact velocity from given height
Here are some sections of textbooks that give a more detailed explanation.
COLLEGE PHYSICS Chapter 2, Motion in One Dimension ⇐ (this is the AP Physics 1 Textbook from 2017-2018)
HALLIDAY FUNDAMENTALS OF PHYSICS Chapter 2, Motion Along a Straight Line
MIT LECTURE, Dr. Walter Lewin MIT 8.01, Lecture 2: Introduction to Kinematics(this is a
Vectors and Scalars
Vectors have magnitude and direction, scalars only have magnitude. Know basic trig rules
and how to decompose vectors (refer to Khan Academy video above). Examples Vectors Scalars Acceleration Time Velocity Volume Momentum Speed Force Mass
A car is traveling at 60 mph to the east. A car is traveling at 60 mph.
Displacement and Distance Traveled
What is the difference between displacement and distance?
● Displacement- how out of place
something is
● Distance- how far something traveled
to get out of place
● Displacement is a vector, but distance is a scalar.
Average Speed and Velocity
● The average speed of travel over a time t is given by the following, where s is the
total distance traveled and t is the duration of travel.
● The average velocity of travel over a time t is given by the following, where s is the
Note: In problems, make sure you read carefully! There is a difference between speed and velocity.
Instantaneous Speed and Velocity
● The instantaneous speed is the speed of an object at a certain instant in time. It is
given by the following, where ∆s is the distance traveled during the extremely short
time period ∆t, which is around that instant in time.
● The instantaneous velocity is the velocity of an object at a certain instant in time. It is
given by the following, where ∆s is the displacement of the object during the
extremely short time period ∆t, which is around that instant in time.
The instantaneous velocity and speed also have a definition related to calculus. Because the
instantaneous speed and velocity can keep changing as time passes, the time interval ∆t
must be extremely small. It must be infinitesimally short, in other words.
So, instead, we can write the instantaneous speed as the derivative of the distance with
respect to t and the instantaneous velocity as the derivative of the displacement with
respect to t.
Acceleration
● Acceleration is the changing of an object’s velocity with time. The average
acceleration over a period of time is defined as the change of the velocity over the change in time. It is a vector quantity with dimensions of length per time squared
and commonly has units m/s2
.
ā = ΔvΔt = t −tf i v −vf i
Instantaneous Acceleration
● The acceleration of an object at a point of time is the object’s instantaneous
a = d sdt2 2
= dvdt
1D Motion with Constant Velocity Graph
The s vs t graph for 1D motion with constant velocity is simply a straight line because the
velocity, or the slope of the graph by definition, is constant. The final position of the object can be calculated as s = s0+ v t .
Question: What would the v vs t graph look like? What does the area under the curve of a v
vs t graph mean?
1D Motion with Constant Acceleration
Acceleration, represented by a, is a vector. In 1D motion, a is a single real number with a
sign, positive or negative. When a > 0, the velocity is increasing. When a < 0, the velocity is decreasing.
The Big Four
These formulas relate velocity, time, displacement, and acceleration. They are the basic equations of kinematics and are used to describe the motion of an object with a constant acceleration. Click here for their derivations.
t vf = v0+ a t at s = v0 + 12 2 as v2 1 = v20+ 2 t s = v +vf2 0 Free Fall
When you drop an apple and a bowling ball in a vacuum, the two experience acceleration
due to Earth’s gravitational pull. All objects on Earth experience roughly the same 1
gravitational acceleration (g = 9.81 m/s2). The sign of the acceleration due to gravity can be
positive or negative; it just depends on which direction is positive.
Note: Using the approximate value, g = 10 m/s2 , is highly suggested on the F=ma and other
physics tests. Approximating g makes for quicker calculations. It is also an easy shortcut on
the AP exam(s); just make sure you specify your value of g on the FRQ.
Vertical Projectiles
Suppose you threw a ball straight up in the air. What does it do?
The ball is a vertical projectile. Let’s set the up direction as the positive direction. Then the
equations that model this situation are as follows:
1The location has an effect on the gravitational acceleration. For example, in Boston, it is 9.80 m/s2. Why?
These look very similar to the big four! I wonder why…?
Exercise: Derive the equation for the time it takes for the projectile to reach the peak of the trajectory. Determine how high the projectile reaches as well.
Terminal Velocity
Why do balloons and feathers seem to drift slowly down at a constant velocity? Well,
objects like balloons and feathers reach their terminal velocities quickly. When an object 2
reaches its terminal velocity, it stays at that velocity and cannot accelerate due to gravity anymore. This happens to skydivers, which typically have a terminal velocity of 200 km/hr. Later after we have learned forces and fluids we will derive the mathematical model.