Acceleration

Physics
acceleration

Agenda:

● Understand Acceleration by testing with a pull

back car.

Do-Now

Take out your chromebook, go to
Lab#22 Pull back car lab

Mini Lab: How did the pull-back toy car move?

What was the car's motion the moment right before you
released it?

Did its speed change from start to finish? If so how did it
change?

Draw a dot diagram for the whole process.

The car did not move with constant velocity.

Hopefully, you observed that..
·the car started from rest(v = 0).
·the car's speed increased.
· it might have changed direction.
· it eventually slowed down.
· it came to a stop(v = 0 again).

Within a reasonable rance, when you pull back more,
and let the car go. Begin from not moving vi=0, the
car reach higher speed in shorter amount of time.
or…
The car speeding up faster.
or…
The car has a larger acceleration.

When you make the graph, is that a straight line?

Change in Velocity

In each second the car traveled one more meter than it did in the previous second

The car's velocity was 1 m/s greater each second.

This is a measure of the change in velocity.

change in velocity = the final velocity – the initial velocity

Acceleration

Acceleration is defined as the rate of change of the velocity

or

the change in velocity .

the time taken to change

Use the symbol "a" to mean acceleration

where

speed

spee
d

change in
direction

Acceleration

Acceleration is a vector, it has direction.
we use the sign (+ or –) to indicate direction:
·Remember that in one-dimension, there are only two directions
(forward/backward, right/left...)

In general, acceleration occurs whenever there is a...
speed increase speed decrease direction change

Uniform Acceleration

Once we solve for the acceleration of an object, we will assume
that it has the same value for the whole problem.

We call that constant acceleration or uniform acceleration,
because it doesn't change.

Is constant acceleration and constant velocity the same?

Changing Velocity

Recall the car that leaked oil every second?
Here are the oil trails left by this car on two trips.

Which trip is at constant speed?

Describe the trip that is not at constant speed.

t [s]

0

1

2

3

4

5

6

7

8

9

10

x [m]

0

5.5

11

16.5

22

27.5

33

38.5

44

49.5

55

What is the Car's Motion During Trip A?

What's happening to the distance traveled each second?

What's happening to the velocity during each second?

position [meters]

The car travels 5.5 meters every second.

The car travels with a constant velocity of 5.5 m/s.

t [s]

0

1

2

3

4

5

6

7

8

9

10

x [m]

0

1

3

6

10

15

21

28

36

45

55

What is the Car's Motion During Trip B?

What's happening to the distance traveled each second?

What's happening to the velocity during each second?

position [meters]

Each second, the car travels 1 more meter than the last second.

The car's velocity is increasing by 1 m/s each second.

SI Units

The unit of acceleration can be found by substituting the units for
velocity and time into the equation

we read this as...

"meters per second - per second"

or

"meters per second squared"

acceleration= change in velocity / time

where

Acceleration

acceleration units are

m/s2

"meters per second - per second"

or

"meters per second squared"

Do the example together.

A cat is speeding up from 0.6 m/s to 2.1 m/s in 3 s;

What is its acceleration?

Looking For

Solution-(Show relationships,
substitutions, solutions, and units)

Given

Formulas

To manipulate the equations

Do-Now
Draw dot diagrams for a car driving to the right that

1. has a positive acceleration(speeding up).
2. has a negative acceleration(slowing down).
3. has a constant velocity.
4. moves super slow.

A school bus driver sees a man crossing the street at an intersection.
The bus driver hits the brake pedal and turns the steering wheel to
avoid him. Which answer describes the acceleration of the bus?

A

It increases speed and changes direction.

B

It decreases speed and changes direction

C

It increases speed and does not change direction.

D

It decreases speed and does not change direction.

Quick review

Acceleration is the rate of change of _________ .

A

displacement

B

distance

C

position

D

velocity

The unit for velocity is:

A

m

B

m/s

C

m/s2

D

m/s3

The unit for acceleration is:

A

m

B

m/s

C

m/s2

D

m/s3

A horse gallops with a constant acceleration of 3 m/s2.
This means that:

A

The horse's velocity doesn't change.

B

The horse moves 3 m every second.

C

The horse's velocity increases 3 m every second.

D

The horse's velocity increases 3 m/s every second.

Solving for Acceleration

1.

A car changes velocity from 10 m/s to 40 m/s in 5 s;

What is its acceleration?

2. A train traveling at 50 m/s to the left changes
velocity to 10 m/s to the right in 15 s. What was the
train's acceleration? (Hint - what do the directions left
and right do to the sign of the velocity?)

Solving for ∆v

3. A car accelerates at 4.5 m/s2 for 8 s; What was the

car's change in velocity?

4. Starting from rest, a train accelerates at 8.0 m/s2 for
9.0 s. What is the train's change in velocity?

Solving for Time

5. A car accelerates at a rate of 5 m/s2 from a velocity of 10
m/s to a velocity of 60 m/s; How much time did it take?

6. A rocket, initially at rest, accelerates at 17 m/s2.
How much time will it take the rocket to achieve a
velocity of 323 m/s?

Check your answer with your neighbors

Example: Solving for vf
7. A car with an initial velocity of 3 m/s accelerates at 4.5 m/s2 for 8 s;

What was the car's final velocity?

8. Starting from rest, a car accelerates at 4 m/s2 for 6 s. What is the
car's final velocity?

Check your answer with your neighbors

Example: Solving for vf

9. A toy car accelerates at a rate of 0.25 m/s2 for 4 s until it reaches a velocity
of 3.5 m/s. What was its initial velocity?

10. An object accelerates at a rate of 3 m/s2 for 6 s until it reaches a
velocity of 20 m/s. What was its initial velocity?

● Take out your chromebook, go to the maze

simulation webpage.

● Explore.

https://phet.colorado.edu/en/simulations/maze-game

Write in detail and think about those factors:
● Position - distance, displacement
● Speed - fast, slow
● Velocity
● Direction - to the direction of moving? opposite direction?
● Acceleration - which direction does it speeding up.

Do-Now
● Take out your chrome book.
● Lab#28, start prelab right away

How will the speed change?

About ramp
What is the initial speed when the ball released from the hill?
We can measure the time it takes for the ball to reach the end.
The gravity didn’t change, so the acceleration will stay the same.

What is the final velocity?

Physics
Acceleration

Agenda:

● the Graph for the lab.

● Direction of acceleration

● Free Fall under gravity

Recall what you
observed in the
ramp lab.

What cause the
ball rolling down
the hill?

Let a car and a car wheel
drop.

Predict:
Which will land first?

What cause it to happen?

Free Fall
What did you observe
when there is air in the
building?

What did you observe
when there is no air in the
building?

How did that happened?

Try:

while the cart is moving forward, give it a force to speed it up. How
can you do it?

while the cart is moving forward, give it a force to slow it down. How
can you do it?

direction of acceleration = direction of the force

direction of velocity = direction the object moving

direction of acceleration = direction of the force

direction of velocity = direction the object moving

Is Acceleration Due to Gravity the Same for

All Objects?

What’s the direction of the acceleration?

Any object that falls only under the influence of gravity is said to be in
Free Fall.

Objects in Free Fall...
·are assumed not to be affected by air resistance
·accelerate downward at 9.8 m/s2.

The acceleration due to gravity is special so we write g instead of a.

a = -g = -9.8 m/s2

To make problem solutions a little easier,
we can approximate g as g = 10 m/s2.

Free Fall

Draw a model of Free Fall

An object is thrown upward
with initial velocity, vi

What happens when it
lands?

What happens at the top?

What happens when it
goes down?

What happens when it
goes up?

It stops momentarily.
v = 0
a = -9.8 m/s2

It returns with the
negative of its initial
velocity, -v0

Draw a model of Free Fall

An object is thrown upward
with initial velocity, vi

It speeds up
(v↓,a↓)
a = -9.8 m/s2

It slows down.
(v↑,a↓)
a = -9.8 m/s2

Assume the objects are in free fall.
1. A cannonball is fired upward with a velocity of 230 m/s.

a.

How fast is it going when it strikes the ground? _________

b.

How fast is it going after 10 s? _________

c.

How much time does it take
to get to its maximum height?

d.

How much time does it take the rock to hit the ground? _________

2. A cannonball is fired straight upward with an initial velocity
of 50 m/s. How much time until the cannonball reaches its
maximum height?

3. An acorn falls from an oak tree. You observe that it takes 3.5
s to hit the ground. How fast was it going when it hit the
ground?

Physics Day 27
Motion in One Dimension

Agenda:

● making v-t graph.

● distance and acceleration on vt graph

Position - Time Graphs

the slope on a
position-time graph (p-t graph) is
the velocity.

Velocity - Time Graphs

What does the dashed
blue line tell us?

Just as we could plot position
versus time, we can plot velocity
versus time.

Velocity - Time Graphs

The dashed line shows the
velocity over time, and that
is constant.

What does that tell us
about the acceleration?

Velocity - Time Graphs

Since acceleration is the
change in velocity over
time, this line tells us that
the acceleration is zero.

The slope of the line is also
zero. What conclusion can
we now make?

the slope on a
velocity-time graph (v-t graph)
is the acceleration.

Velocity - Time Graphs

Velocity - Time Graphs
1.

Velocity - Time Graphs
2.

v [m/s]

3. What is the acceleration represented on the
velocity vs. time graph?

v [m/s]

3. What is the acceleration represented on the
velocity vs. time graph?

Do-Now

Describe the following motion using following words:
speed

velocity

acceleration

time

distance constant

Do-Now

.

Do-Now

Describe the motions below.
Using words:
● speed
● acceleration
● time
● distance