1. Chapter 10: Motion 10.1 An object in motion changes position
10.2 Speed measures how fast position changes
10.3 Acceleration measures how fast velocity changes

2. 10.3 Acceleration measures how fast velocity changes
Before, you learned:
Speed describes how far an object travels in a given time
Velocity is a measure of the speed and direction of motion
Now, you will learn:
How acceleration is related to velocity
How to calculate acceleration

3. Speed and direction can change with time
Throw a ball in the air, it comes back down, bounces on the ground - the speed and direction are constantly changing
You can find out an object’s position change during a certain amount of time if you know the velocity
Can also measure how an object’s velocity changes with time:
Acceleration: The rate at which velocity change with time – how quickly velocity is changing
Constant 30 km/hr trip: acceleration = ?

4. Acceleration
Typically “speeding up”, but can be any change in velocity
A car slowing down is accelerating
A runner turning a corner, yet at constant speed, IS accelerating – direction of velocity has changed
A vector - size & direction…a change being slow down, speed up, or turn

5. Acceleration 1. Acceleration in the same direction as motion
The speed of the object increases
2. Acceleration in the opposite direction of motion
The speed of the object decreases
3. Acceleration at a right angle to motion
The direction of motion changes (speed can stay the same)

6. Acceleration can be calculated from velocity and time
A race: in 1 s, you go from standing still to running 6 m/s, while your classmate goes from 0 m/s to 3 m/s
How did velocity change over time?
Compare the initial and final velocities
Know the time interval over which the velocity changed
Acceleration = ??
What if classmate goes from 3 to 6 m/s in 1 s?
As long as the velocity is increased by 3 m/s, the acceleration remains the same.

7. Calculating Acceleration
Know the initial and final velocities, and the time interval
Acceleration (m/s2) = [final velocity (m/s) – initial velocity (m/s)]
time (s)
a = vfinal – vinitial m/s2 = (m/s – m/s) = (m - m) * 1
t s s s s
1. A train traveling at 10 m/s slows down to a complete stop in 20 s. What is the acceleration of the train?
2. Man walking 0.5 m/s accelerates to 0.6 m/s in 1 s.
You know:
You want to know:
Formula:
Substitute:
Calculate:
Check your units:

8. Calculating Acceleration
Know the initial and final velocities, and the time interval
Acceleration (m/s2) = [final velocity (m/s) – initial velocity (m/s)]
time (s)
a = vfinal – vinitial m/s2 = m/s – m/s = (m - m) * 1
t s s s s
A man walking 0.5 m/s accelerates to 0.6 m/s in 1 s. What is his acceleration?
You know:
You want to know:
Formula:
Substitute:
Calculate:
Check your units:

9. Acceleration over Time
Even a very small acceleration can lead to great speeds if given enough time
Deep Space 1: acceleration < m/s2
over 20 months speed is increased by 4500 m/s (10,000 mi/h)
Although the thrust from the engine is less pressure than the weight of a single sheet of paper in the hand, each day it will add between 15 mph to 20 mph to the probe's speed.
In 300 days it will have accelerated the Deep Space One by 60,000 mph

10. Velocity-time graphs Acceleration = velocity / time
The distance an object travels depends on its velocity

12. Velocity Time Graph
Calculate how far the ball traveled: Distance = velocity * time
V= 200cm/s, t = .2s D = 40 cm (A = bxh area under the “curve”)

13. Velocity Time Graph
Acceleration (m/s2) = [final velocity (m/s) – initial velocity (m/s)]
time (s)
Question: Consider the motion of the object whose velocity-time graph is given in the diagram.
What is the acceleration of the object between times        and       ?
What is the acceleration of the object between times          and         ?
What is the net displacement of the object between times        and         ?
area