CHAPTER 3 ACCELERATION

Defining Acceleration:

-Term

-Motion Diagram

-Graphic Relationships

-Kinematic equations

Acceleration : the rate change in speed ‘How fast something will get faster’Units: m/s2 or km/hr2

constant velocity 1s 1s 1s 1s

1s 1s 1s 1s

constant acceleration

Graphic Relationship

Constant speed Constant Acceleration

D (m) V (m/s)

t (s) t (s)

Graphic Relationship

D V

Constant Speed Zero Acceleration

t t

D V

Constant Speed Zero Acceleration

t t

Graphic Relationship

Variable speed Constant acceleration

D V

t t

Velocity v. Acceleration

An object at the 50 m mark is at rest for 10 s. Then moves back to the origin in 50 s where it remains at rest for 10 s. It then moves is the forward direction moving at a constant 1.5 m/s. Finally the object moves 100 m in 10 s at a constant speed. Draw a distance to time graph and then a velocity to time graph to represent this situation.

Velocity v. Acceleration

Motion DiagramsUses vector relationships to define acceleration

NOTE: Acceleration is the change in the velocity in the change in time.

vi vf

vf – vi = negative change in velocity or vi Since time is constant (+)

- a vf

Motion Diagrams

vi vf

vf – vi = positive change in velocity or

Vf

+a vi

A dog runs into a room and sees a cat at the other end of the room. The dog instantly stops but slides along the wooden floor at a constant acceleration until it stops. Draw the motion diagram.

Kinematic Equations

Average Acceleration:a = ∆v / ∆t or∆v = a∆t

Final velocity at a constant acceleration in time:vf = vi + a∆t

Final velocity at a constant acceleration in a distance:

vf2 = vi

2 + 2a∆d

Kinematic Equations

Distance traveled at a constant acceleration in a defined time:

∆d = vi∆t + ½ a∆t2

Acceleration with Kinematic Equations

1. What is the average rate of acceleration for a ball traveling from 5 m/s to 0.25 m/s in 5 s?

2. How does the answer in #1 describe the motion of the ball?

3. A car gets a rolling start. The velocity of the car goes from 15 mile/hr to 68 mile/hr in 4.2 s. What is the average rate of acceleration?

4. To avoid hitting another car, you break changing your velocity from 36 m/s to 3.2 m/s in 2.8 s. What is your average acceleration?

Acceleration and Kinematic Equations

5. What final velocity would an object obtain at a constant acceleration of 0.25 m/s2 for 54s starting from rest?

6. A rocket traveling at a constant velocity of 125 m/s fires it boosters and accelerates at a constant 5.2 m/s2 for 2.55 s before the boosters shuts down. What is the final velocity of this rocket?

Acceleration with Kinematic Equations

7. How far will an object travel at a constant acceleration of 0.55 m/s2 in 0.75 minutes starting from rest?

8. If the object in #7 began at a initial velocity of 2.5 m/s, how far would the object travel in the same time interval?

9. What is the final velocity of a car that accelerates at a constant 0.25 m/s2 for 300 m starting for rest?

10. A car is seen rolling down a hill staring at an initial velocity of 0.15 m/s. What would the final velocity of the car be if it accelerates at 0.25 m/s2 for 150 m?

Acceleration with Kinematic Equations

11. A grocery cart is rolling down the parking lot at a constant .85m/s. How far will the cart roll at an acceleration of 0.15 m/s2 in a time interval of 32 s?

12. An object is moving at a constant 5.5 m/s when the wind slows the object at a rate of 0.75 m/s2 for a distance of 250 m. What would the final velocity of the object be?

13. A driver of a car traveling at 35 mil/hr sees a child in the road 53 m from the car when he begins to break. If he accelerates at -11.25 m/s2 for 32s , will the car hit the child?

Free Fall

Free Fall: refers to an object acting under the influence of gravity without air resistance.Acceleration due to gravity (g) = 9.8 m/s2

*****If up is the positive direction, then –g*****

If down is the positive direction, then +g

Free Fall

An object in free fall has a (+) acceleration (+9.8 m/s2)Object dropped = +9.8 m/s2

Object thrown up - = - 9.8 m/s2 (against gravity)

Velocity in the downward direction will be (+), when up is (-)

Velocity in the upward direction will be (-)Vf = 0 m/s at the peak

Kinematic Equations for Free Fall

Average Acceleration:∆v = g∆t

Final velocity at a constant acceleration in time:

vf = vi + g∆t

Final velocity at a constant acceleration in a distance:

vf2 = vi

2 + 2g∆d

Distance traveled at a constant acceleration in a defined time:

∆d = vi∆t + ½ g∆t2

Free Fall Sample Problems

1. An object at a state of rest is released and falls for 1.5 s. What is the velocity of the object at the end of the 1.5 s?

2. How far will the object have fallen?3. An object is dropped from a defined

height. What is the velocity of the object at the 4 s interval?

4. What is the distance traveled by the object in #3 above?

5. A ball is dropped from a 5.5 m high window. How fast is the ball moving after this distance?

Free Fall Sample Problems

6. A ball is thrown straight up at an initial velocity of 12.5 m/s. If the velocity of the ball is considered zero at the highest point, what is the highest point?

7. How much time elapse for the ball to reach the highest point in #6 above?

8. Considering the definition of free fall, how much time will elapse for the ball to travel to its highest point and return to the thrower?

9. A ball is thrown straight up and reaches it’s highest point at 1.5 m. What was the initial velocity?