Linear Motion

Chapter 2

Review time!

• Remember when we were using math in physics….

Vectors vs Scalars

• Scalars are quantities that have a _______, or numeric value which represents a size Examples of these are:_______________

• Vectors are quantities which have a ___________ and a ______, Examples of these are:_______________

Measuring how fast you are going

• Speedv• Scalar• Standard unit is m/s

• Velocityv• Vector• Standard unit is m/s,

plus direction

t

d

time

ntdisplacemev

t

d

time

distancev

Velocity and Speed

• If it take the person 4 seconds to walk around the square, what is her average speed and average velocity?

• For speed, d=12m and t=4s, so v=3m/s

• For velocity, d=0 and t=4s, so v=0m/s

Practice Problem

• A boy takes a road trip from Philadelphia to Pittsburgh. The distance between the two cities is 300km. He travels the first 100km at a speed of 35m/s and the last 200km at 40m/s. What is his average speed?

1st step. ID important info

• A boy takes a road trip from Philadelphia to Pittsburgh. The distance between the two cities is 300km. He travels the first 100km at a speed of 35m/s and the last 200km at 40m/s. What is his average speed?

Different types of velocity and speed

• Average velocity/speed• A value summarizing

the average of the entire trip.

• All that’s needed is total displacement/distance and total time.

• Instantaneous velocity• A value that

summarizes the velocity or speed of something at a given instant in time.

• What the speedometer in your car reads.

• Can change from moment to moment.

What are we looking for

• Although we are looking for average speed…we first need to find time. hrt

t

t

dV

86.2

10035

hrtt

t

dV

5

20040

Total time 7.86 hr

Using the total time, you can calculate an average velocity 38.17

hr

km

Acceleration

t

vv

t

vonacceleratia if

• Change in velocity

over time.• Either hitting the gas

or hitting the break counts as acceleration.

• Units are m/s2

delta.• Means “change in”

and is calculated by subtracting the initial value from the final value.

Acceleration(vector)

The rate of change in velocity.

-Accelerations cannot happen with out the presence of a force (a push or a pull)

-Acceleration will depend on the direction of this force

-Constant acceleration is when, in a given amount of time, acceleration does not change

force

acceleration

force

acceleration

Acceleration(continued)

Positive acceleration is caused by a force in the positive direction.

-Depending on the initial movement of an object, a positive acceleration will either speed up or slow down an object.

- if the object starts at rest or is already moving positively, it will speed up.

-If the object is moving in the negative direction, a positive acceleration will slow the object down.

Acceleration(continued)

Negative acceleration is caused by a force in the Negative direction.

-Depending on the initial movement of an object, a negative acceleration will either speed up or slow down an object.

- if the object starts at rest or is already moving negatively, it will speed up.

-If the object is moving in the positive direction, a negative acceleration will slow the object down.

Rules for using linear motion equations

• We always assume that acceleration is constant.

• We use vector quantities, not scalar quantities.• We always use instantaneous velocities, not

average velocities• Direction of a vector is indicated by sign.

Incorrect use of signs will result in incorrect answers.

Practice Problem

A car going 15m/s accelerates at 5m/s2 for 3.8s. How fast is it going at the end of the acceleration?

First step is identifying the variables in the equation and listing them.

Practice Problem

A car going 15m/s accelerates at 5m/s2 for 3.8s. How fast is it going at the end of the acceleration?

t=3.8s

vi=15m/s

a=5m/s2

vf=?

Practice Problem 2

• A penguin slides down a glacier starting from rest, and accelerates at a rate of 7.6m/s2. If it reaches the bottom of the hill going 15m/s, how long does it take to get to the bottom?

Practice Problem 2

• A penguin slides down a glacier starting from rest, and accelerates at a rate of 7.6m/s2. If it reaches the bottom of the hill going 15m/s, how long does it take to get to the bottom?

Equation for displacement

t

dv

2

fi vvv

tvd

t

vvd fi

2

Two versions of the same average velocity equations

One more way to calculate average velocity

Although this equation is not used often, it is important to derive other useful equations!

Equation that doesn’t require vf

t

vvd fi

2

atvv if

t

atvvd ii

2

)2(2

1atvtd i

2

2

1attvd i

Combine

Practice Problems

A ball rolling up a hill accelerates at –5.6m/s2

for 6.3s. If it is rolling at 50m/s initially, how farhas it rolled?

If a car accelerates at a rate of 4.64m/s2 and it travels 162m in 3s, how fast was it going

initially?

An equation not needing t tvvd fi 2

1atvv if

atvv if

ta

vv if

a

vvvvd iffi2

1

a

vvd if

22

21

advv if 222

Combine

A bowling ball is thrown at a speed of

6.8m/s. By the time it hits the pins 63m

away, it is going 5.2m/s. What is the

acceleration?

advv if 222

The Big 3

atvv if advv if 222

2

2

1attvd i

Problem Solving Steps

• Draw a quick sketch• Identify givens in a problem and write them down.• Determine what is being asked for and write

down with a questions mark.• Select an equation that uses the variables (known

and unknown) you are dealing with and nothing else.

• Solve the selected equation for the unknown.• Fill in the known values and solve equation• Make a chart like this one…if its helpful

Gravity• Gravity causes an acceleration.• All objects have the same acceleration due

to gravity.• Differences in falling speed/acceleration

are due to air resistance, not differences in gravity.

• g=9.8m/s2 down• When analyzing a falling object, consider

final velocity before the object hits the ground and initial velocity the instant the object is dropped

Hidden Variables

• Objects falling through space can be assumed to accelerate at a rate of 9.8m/s2 down.

• Starting from rest corresponds to a vi=0

• Coming to a stop corresponds with a vf=0

• A change in direction indicates that at some point v=0.

• Dropped objects have no initial velocity.

Practice Problem

• A ball is dropped and hits the ground with a velocity of at a speed of 25m/s. How far has it traveled when it reaches the ground?

vi=0 m/s

vf=25 m/s

a=g=9.8m/s2

d=?

t=?

A plane slows on a runway from 207km/hr

to 35km/hr in about 5.27km.

a. What is its acceleration?

b. How long does it take?

An onion falls off an 84m high cliff. How

long does it take him to hit the ground?

An onion is thrown off of the same cliff at

9.5m/s straight up. How long does it take

him to hit the ground?

A train engineer notices a cow on the

track when he is going 40.7m/s. If he can

decelerate at a rate of -1.4m/s2 and the

cow is 500m away, will he be able to stop

in time to avoid hitting the cow?

Practice Problems

• A car slows from 45 m/s to 30m/s over 6.2s. How far does it travel in that time?

• A cyclist speeds up from his 8.45m/s pace. As he accelerates, he goes 325m in 30s. What is his final velocity?