1. Section 3: Acceleration
Acceleration describes how the velocity of an object is changing with time. K
What I Know W
What I Want to Find Out L
What I Learned

2. Essential Questions How are acceleration, time, and velocity related?
What are three ways an object can accelerate?
How can an object’s acceleration be calculated?
What are the similarities and differences between straight line motion, circular motion, and projectile motion?
Copyright © McGraw-Hill Education
Acceleration

3. Vocabulary Review New velocity acceleration centripetal acceleration
Copyright © McGraw-Hill Education

4. Acceleration, Speed and Velocity
Acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating.
A change in velocity can be either a change in how fast something is moving or a change in the direction it is moving.
Acceleration occurs when an object changes its speed, its direction, or both.
Copyright © McGraw-Hill Education
Acceleration

5. Speeding Up and Slowing Down
If the acceleration is in the same direction as the velocity, the speed increases.
Acceleration
Copyright © McGraw-Hill Education

6. Speeding Up and Slowing Down
If the speed decreases, the acceleration is in the opposite direction from the velocity, and the acceleration is negative.
Acceleration
Copyright © McGraw-Hill Education

7. Calculating Acceleration
To calculate the acceleration of an object, the change in velocity is divided by the length of time interval over which the change occurred.
To calculate the change in velocity, subtract the initial velocity (vi)—the velocity at the beginning of the time interval—from the final velocity—the velocity at the end of the time interval (vf). ­
Copyright © McGraw-Hill Education
Acceleration

8. Calculating Acceleration
Using this expression for the change in velocity, the acceleration can be calculated from the following equation:
Acceleration
Copyright © McGraw-Hill Education

9. CALCULATE ACCELERATION
SOLVE FOR THE UNKNOWN
Set Up the Problem
a = (vf –vi ) t = (0 m/s – 3 m/s) 2 s west
Solve the Problem
a = (0 m/s – 3 m/s) 2 s = – 1.5 m/s2 west
The acceleration has a negative sign, so the direction is reversed.
a = – 1.5 m/s2 east
Use with Example Problem 3.
Problem
A skateboarder has an initial velocity of 3 m/s west and comes to a stop in 2 s. What is the skateboarder’s acceleration?
Response
ANALYZE THE PROBLEM
KNOWN
initial velocity: vi = 3 m/s west
final velocity: vf = 0 m/s west
time: t = 2 s
UNKNOWN
acceleration: a
EVALUATE THE ANSWER
The magnitude of the acceleration (1.5 m/s2) is reasonable for a skateboard that takes 2 s to slow from 3 m/s to 0 m/s. The acceleration is in the opposite direction of the velocity, so the skateboard is slowing down, as we expected.
Copyright © McGraw-Hill Education
Acceleration

10. Speeding Up
Suppose a car starts at rest and reaches a speed of 80 m/s as it heads east down the street. Its acceleration can be calculated as follows:
Acceleration
Copyright © McGraw-Hill Education

11. The final speed is zero and the initial speed was 3 m/s.
Slowing Down
Now imagine a skateboarder is moving in a straight line with a velocity of 3 m/s north and comes to a stop in 2 s.
The final speed is zero and the initial speed was 3 m/s.
Copyright © McGraw-Hill Education
Acceleration

12. Calculating Negative Acceleration
The skateboarder's acceleration is calculated as follows:
The acceleration is in the opposite direction of the skateboard’s velocity when the skateboarder is slowing down.
Copyright © McGraw-Hill Education
Acceleration

13. Changing Direction
The speed of the horses in this carousel is constant, but the horses are accelerating because their direction is changing constantly. Acceleration toward the center of a curved or circular path is called centripetal acceleration.
Acceleration
Copyright © McGraw-Hill Education

14. Projectile Motion
Anything thrown or shot through the air is called a projectile. Projectiles follow a curved path because they have horizontal and vertical velocities. The projectile’s horizontal velocity is constant. It has vertical velocity downward due to gravity.
Acceleration
Copyright © McGraw-Hill Education

15. Review Essential Questions Vocabulary
How are acceleration, time, and velocity related?
What are three ways an object can accelerate?
How can an object’s acceleration be calculated?
What are the similarities and differences between straight line motion, circular motion, and projectile motion?
Vocabulary
acceleration
centripetal acceleration
Copyright © McGraw-Hill Education
Acceleration