MOTION UNITUNIT #3 – CHAPTER #8.2 – AVERAGE VELOCITY

Objectives

Be able to calculate average velocity, displacement, and time interval for an object in uniform motion, given appropriate data

HOW COULD YOU DEFINE SPEED, OR VELOCITY?

What do you notice when you move fast or when you move slow?

What do you notice about objects that move fast or move slow?

TRY TO DESCRIBE IN TERMS OF POSITION AND TIME.

SPEED AND VELOCITY, WHATS THE DIFFERENCE?

Can two objects have the same speed and different velocities?

Velocity is a vector – has direction and magnitude

Speed is a scalar, it only has magnitude.

SPEED AND VELOCITY A) B)

Is the speed the same for A and B?

Is the velocity the same for A and B?

Objects at the same speed can have different velocities.

Speed can be called the magnitude of the velocity.

AVERAGE VELOCITY

Copy these two formulas in your notes! Average velocity is equal to the change in

position (displacement) divided by the change in time.

This is why velocity has the units (m/s)

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WHY DO WE SAY AVERAGE VELOCITY, INSTEAD OF JUST VELOCITY?

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AVERAGE VELOCITY

In a way, average velocity is a simplification.

It tells us on average over a certain time interval how fast an object is moving.

It does not tell us exactly what velocity the object moved at for all instants in that interval.

DIFFERENCE BETWEEN AVERAGE VELOCITY AND AVERAGE SPEED.

I walk 10 m North in 5 seconds and then walk for 10 m South in the next 5 seconds.

What is my average velocity? My average speed?

Graphically Mathematically

Calculating Average VelocityThe relationship between average velocity,

displacement, and time is given by:

Use the above equation to answer the following questions.

1. What is the average velocity of a dog that takes 4.0 s to run forward 14 m?

(3.5 m/s forward)2. A boat travels 280 m east in a time of 120 s. What

is the boat’s average velocity?(2.3 m/s east)

v av

d

t

Calculating DisplacementThe relationship between displacement, average velocity,

and time is given by:

Use the above equation to answer the following questions.

1. What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s?

(120 m [N])

2. A person, originally at the starting line, runs west at 6.5 m/s. What is the runner’s displacement after 12 s?

(78 m west)

d

v av t

Calculating TimeThe relationship between time, average velocity, and

displacement is given by:

Use the above equation to answer the following questions.

1. How long would it take a cat walking north at 0.80 m/s to travel 12 m north?

(15 s)

2. A car is driving forward at 15 m/s. How long would it take this car to pass through an intersection that is 11 m long?

(0.73 s)

t d

v av

CONVERTING UNITS:m/s <-> Km/h

Remember unit analysis with Mr. Baron? Here it is in science!

For example, convert 75 km/h to m/s.

Converting between m/s and km/h

Try the following unit conversion problems.

1. Convert 95 km/h to m/s.

(26 m/s)

2. A truck’s displacement is 45 km north after driving for 1.3 h. What was the truck’s average velocity in km/h and m/s?

(35 km/h [N], 9.6 m/s [N])

3. What is the displacement of an airplane flying

480 km/h [E] during a 5.0 min time interval?

(40 km [E] or 40, 000 m [E])

PROBLEM #1:

What is the average velocity of a skateboard that goes 50 m [W] over a time interval of 8 seconds?

Answer: Average Velocity = 6.25 m/s [W]

PROBLEM #2

If a cyclist can go the same distance in a time interval of 4 seconds, how much greater is her average velocity than the skateboarder’s average velocity?

Double the velocity of the skateboarder;Average velocity = 12.5 m/s [W]

PROBLEM #3

A deer is running forward at a speed of 46 km / h. How far does it travel in 30 seconds?

Displacement = 0.38 km or 380 meters [forward]

PROBLEM #4:

How many minutes would it take a car moving at an average velocity of 82 km / h to travel 125 km?

Time = 91 minutes