MOTION

4.3 AccelerationAcceleration is the rate at which your

speed (or velocity) changes.

4.3 AccelerationWhat is the bike’s acceleration?

4.3 AccelerationAcceleration describes how quickly speed changes.

Acceleration is the change in speed divided by the change in time.

4.3 Speed and accelerationAn acceleration of

20 km/h/s means that the speed increases by 20 km/h each second.

The units for time in acceleration are often expressed as “seconds squared” and written as s2.

Can you convert this rate using conversion

factors?

Solving Problems

A sailboat moves at 1 m/s.

A strong wind increases its speed to 4 m/s in 3 s.

Calculate acceleration.

1. Looking for: …acceleration of sailboat

2. Given: …v1 = 1 m/s; v2 = 4 m/s; time = 3 s

3. Relationships: a = (v2 – v1)/t

4. Solution: a = (4 m/s – 1 m/s)/ 3 s = 1

m/s2

Solving Problems

s

sm

3

/ 3

Your Turn (#1)Calculate the acceleration of an airplane that

starts at rest and reaches a speed of 45 m/s in 9 seconds.

1.Given: V1=0 m/s, V2 = 45 m/s, t=9s

2.Relationships: a = (v2 – v1)/t

3.Solution: a = (45 m/s – 0 m/s)/ 9 s s

sm

9

/ 45 = 5

m/s2

Your Turn (#2)Calculate the acceleration of a car that slows

from 50 m/s to 30 m/s in 10 seconds.

1.Given: V1=50 m/s, V2 = 30 m/s, t=10s

2.Relationships: a = (v2 – v1)/t

3.Solution: a = (30 m/s – 50 m/s)/ 10 s

s

sm

10

/ 20 = -2

m/s2

Practice #1While traveling along a highway, a driver slows from

24 m/s to 15 m/s in 12 seconds. What is the automobile’s acceleration? (Remember that a negative value indicates a slowing down or deceleration.)

Given: V1=24 m/s, V2 = 15 m/s, t=12s

2.Relationships: a = (v2 – v1)/t

3.Solution: a = (15 m/s – 24 m/s)/ 12 s

s

sm

12

/ 9 = -0.75

m/s2

Practice #2A parachute on a racing dragster opens and changes

the speed of the car from 85 m/s to 45 m/s in a period of 4.5 seconds. What is the acceleration of the dragster?

1.Given: V1=85 m/s, V2 = 45 m/s, t=4.5s

2.Relationships: a = (v2 – v1)/t

3.Solution: a = (45 m/s – 85 m/s)/ 4.5 s

s

sm

5.4

/ 40 = -8.9 m/s2

Practice #4A car traveling at a speed of 30.0 m/s encounters an

emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at

–4.0 m/s2?

Given: V1=30 m/s, V2 = 0 m/s, a= -4.0 m/s2, t=??

2.Relationships: a = (v2 – v1)/t

3.Solution: t = (0 m/s – 30 m/s)/ -4.0 m/s2

2/ 0.4

)/30/0(

sm

smsm

= 7.5 s

)v(v if taa

)vv( if t

2/ 0.4

)/30(

sm

sm

Practice #5If a car can go from 0 to 60. mph in 8.0 seconds,

what would be its final speed after 5.0 seconds if its starting speed were 50. mph?

How will we solve this one?This is a 2-part question Solve for the Acceleration, “a” with the first part.Solve for Vf given the Vi=50mph, and the “a” you

calculated.

4.3 Acceleration on speed-time graphs

Positive acceleration adds more speed each second.

Things get faster. Speed increases

over time.

4.3 Acceleration on speed-time graphs

Negative acceleration subtracts some speed each second.

Things get slower. People sometimes

use the word deceleration to describe slowing down.

4.3 Acceleration on position-time graphs

The position vs. time graph is a curve when there is acceleration.

The car covers more distance each second, so the position vs. time graph gets steeper each second.

4.3 Acceleration on position-time graphs

When a car is slowing down, the speed decreases so the car covers less distance each second.

The position vs. time graph gets shallower with time.

4.3 Free fallAn object is in

free fall if it is accelerating due to the force of gravity and no other forces are acting on it.

4.3 Free fallFalling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2

4.3 Acceleration and direction A car driving around a curve at a

constant speed is accelerating because its direction is changing.

4.3 Curved motionA soccer ball is an

example of a projectile.

A projectile is an object moving under the influence of only gravity.

The path of the ball makes a bowl-shaped curve called a parabola.

4.3 Curved motion

Circular motion is another type of curved motion.

An object in circular motion has a velocity vector that constantly changes direction.