Chapter 2 Section 2:

Acceleration

Motion Review

Speed is the rate that an object’s distance changes Distance is how far an object has travelled

Speed = distance/time

Velocity is rate that an object’s displacement changes Displacement is how far the object is from the starting point

Velocity = displacement/time

When an object travels in only one direction, it’s distance and displacement are the same! This means that the value of speed and velocity would also be the same. From this point on, we will assume that objects are moving in one

direction away from a starting point and therefore we will refer to velocity as a “speed” with a direction to stay consistent with your book.

Speed vs. Time Graphs

What would a speed vs. time graph look like for:

An object with a constant speed?

An object speeding up?

An object slowing down?

Spee

d (

m/s

)

Time (s)

What is the object’s

speed at this point?

0 m/s

Acceleration

Acceleration is the rate of change of velocity

When the velocity of an object changes, we call that

acceleration

Because we are calling velocity a “speed” with direction,

acceleration occurs when there is a change in how fast an

object is moving (speeding up or slowing down), the direction

in which it is moving, or both

Positive Acceleration

Positive acceleration occurs when an object is

speeding up

Acceleration is in the same direction as the velocity

Negative Acceleration

Negative acceleration occurs when an object is

slowing down

Acceleration is in the opposite direction of velocity

We do not call negative acceleration deceleration!

Changing Direction

Any time an object changes direction, it’s velocity

changes even if it is travelling at a constant speed

This also means that acceleration changes when an object

changes direction even if it is travelling at a constant speed

Graphing Acceleration

Because acceleration is a change in velocity over

time, we can use speed vs. time graphs to

determine if acceleration is positive or negative or if

there is no acceleration happening

Based on what you know about acceleration,

which graph(s) illustrate positive and negative

acceleration?

Sp

eed

(m

/s)

Time (s)

Sp

eed

(m

/s)

Time (s) S

pee

d (

m/s

) Time (s)

Negative

Acceleration

No

Acceleration

Positive

Acceleration

Calculating Acceleration

Acceleration is a change in velocity over time.

acceleration (m/s2) = ∆𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (

𝑚

𝑠)

𝑡𝑖𝑚𝑒 (𝑠)

or

acceleration (a) = 𝐹𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑣𝑓 −𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑣𝑖

𝑡𝑖𝑚𝑒 (𝑡)

or

a = 𝑣𝑓 − 𝑣𝑖

𝑡

𝒗𝒇 − 𝒗𝒊

t a

or m/s/s

Acceleration Practice

1. If a race car goes from 0 to 50 m/s in 5 seconds, what is its acceleration?

a = 𝑣𝑓 − 𝑣𝑖

𝑡

a = 50

𝑚

𝑠 −0

𝑚

𝑠

5 𝑠

a = 50

𝑚

𝑠

5 𝑠

a = 10 m/s2

vi = 0 m/s vf = 50 m/s t = 5 s a = ?

For each problem:

List the givens

List the formula you will use

Write the givens in your formula, including units

Show all math calculations

List appropriate units on your final answer

More Acceleration Practice

2. If a car travels at 26 m/s and hits the brakes for 4

seconds to come to a complete stop, what is its

acceleration?

For each problem:

List the givens

List the formula you will use

Write the givens in your formula, including units

Show all math calculations

List appropriate units on your final answer

vi = 100 m/s vf = 0 m/s t = 2 s a = ?

a = 𝑣

𝑓 − 𝑣𝑖

𝑡

a = 0

𝑚

𝑠 −26

𝑚

𝑠

4 𝑠

a = −26

𝑚

𝑠

4 𝑠

a = - 6.5 m/s 2

More Acceleration Practice

3. If a person can accelerate from rest at 2 m/s2, how fast will he be running after 2 seconds?

For each problem:

List the givens

List the formula you will use

Write the givens in your formula, including units

Show all math calculations

List appropriate units on your final answer

vi = 0 m/s vf = ? t = 5 s a = 2 m/s2

𝑣𝑓 − 𝑣𝑖 = a x t

𝑣𝑓 − 0 𝑚/𝑠 = 2 m/s2 x 2 s

𝒗𝒇= 4 m/s

More Acceleration Practice

4. How long would it take a race car to go from 0 m/s to 45 m/s if it can accelerate at 6 m/s2?

For each problem:

List the givens

List the formula you will use

Write the givens in your formula, including units

Show all math calculations

List appropriate units on your final answer

vi = 0 m/s vf = 45 m/s t = ? a = 6 m/s2

t = 𝑣

𝑓 − 𝑣𝑖

𝑎

t = 45

𝑚

𝑠 −0

𝑚

𝑠

6 𝑚/𝑠2

t = 45

𝑚

𝑠

6 𝑚/𝑠2

t = 7.5 s

More Acceleration Practice

5. If a skier is going downhill with an acceleration of 3 m/s2 and has a velocity of 18 m/s after 3 seconds, what was her initial velocity?

For each problem:

List the givens

List the formula you will use

Write the givens in your formula, including units

Show all math calculations

List appropriate units on your final answer

vi = ? vf = 18 m/s t = 3 s a = 3 m/s2

𝑣𝑓 − 𝑣𝑖 = a x t

18 𝑚/𝑠 − 𝑣𝑖= 3 m/s 2 x 3 s

𝒗𝒊= 9 m/s 18 𝑚/𝑠 − 𝑣𝑖= 9 m/s

−𝑣𝑖= - 9 m/s