1. Methods of Motion -Acceleration
AP Physics

2. Average Acceleration
Acceleration is the RATE at which VELOCITY changes.
A truck accelerates from 10 m/s to 30 m/s in 2.0 seconds. What is the acceleration?
Suppose the same truck then slows down to 5 m/s in 2 seconds. What is the acceleration?
“m/s/s” or “m/s2” is the derived unit for acceleration.

3. What do the “signs”( + or -) mean?
Quantity
Positive
Negative
Displacement
You are traveling north, east, right, or in the +x or +y direction.
You are traveling south, west, left, or in the –x or –y direction.
Velocity
The rate you are traveling north, east, right, or in the +x or +y direction.
The rate you are traveling south, west, left, or in the –x or –y direction.
Acceleration
Your speed is increasing in a positive direction or your speed is decreasing in a negative direction.
Your speed is decreasing in a positive direction or your speed is increasing in a negative direction.
Show velocity/acceleration vectors – Scientists and Engineers fig 2.9

4. Beware – the signs can confuse!
Suppose a ball is thrown straight upwards at 40 m/s. It takes 4 seconds to reach its maximum height, then another 4 seconds back down to the point where it was thrown. Assume it is caught with the same speed it was thrown. Calculate the acceleration upwards and downwards.
This negative sign came from using the DELTA
This negative sign came from the DIRECTION of the velocity.
It is no surprise you get a negative answer both ways as gravity acts DOWNWARDS no matter if the ball goes up or down. It is GRAVITY which changes the ball’s velocity.

5. Instantaneous Velocity
Instantaneous velocity is a measure of an object’s displacement per unit time at a particular point in time.
On an x v. t graph, slope of a line at a given point is the instantaneous velocity.
The term velocity alone means instantaneous velocity.
All motion is translational?

6. Instantaneous Acceleration
Instantaneous acceleration is a measure of an object’s velocity per unit time at a particular point in time.
On a vel v. t graph, slope of a line at a given point is the instantaneous acceleration.
The term acceleration means instantaneous acceleration.

7. Graphing Summary v (m/s) a (m/s/s) x (m) t (s) t (s) t (s) slope = v
slope = a
area = Δv
area = Δx
t (s)
t (s)
t (s)

8. Graphing Activity
Analyze the motion of the following cars with position, velocity, and acceleration graphs.
Sketch your predictions on the whiteboards.
Things to consider:
Constant velocity?
Constant acceleration?

10. The 3 Kinematic Equations
There are 3 major kinematic equations than can be used to describe the motion in DETAIL. All are used when the acceleration is CONSTANT.

11. Constant Acceleration
When acceleration is constant the average velocity is just the average of the initial and final velocity values.

13. Calculus of Kinematics
Derivative
Slope on a graph
Integral
Area under curve on a graph
Don’t forget limits of integration

15. Kinematics -Free Fall
AP Physics

16. “g”– The Acceleration due to gravity
The acceleration due to gravity is a special constant that exists in a VACUUM, meaning without air resistance. If an object is in FREE FALL, gravity will CHANGE an objects velocity by 9.8 m/s every second.
The acceleration due to gravity:
ALWAYS ACTS DOWNWARD
IS ALWAYS CONSTANT near the surface of Earth

17. Kinematics for the VERTICAL Direction
All 3 kinematics can be used to analyze one dimensional motion in either the X direction OR the y direction.

18. Acceleration of gravity units
g – represents acceleration
g – gravitational field interactions
All objects accelerate towards Earth, under free-fall conditions, at the same rate.
Gravitational fields force masses to move in a direction towards Earth.