Speed and Velocitypg. 5 in NB

Objectives• Describe one dimensional

motion using equations for speed and velocity.

• Analyze one dimensional motion using equations for speed and velocity.

• Define and identify positive and negative velocities.

Terms• Speed• Velocity

Equations

•Speed is the distance traveled divided by the time taken.

•V speed•d distance•t time

•Velocity is the change in position divided by the change in time.

•V velocity• change in position• change in time

Rearranging Formulas Speed

𝑉=𝑑𝑡

• Solve for distance

• Solve for time

Rearranging Formulas Velocity

• Solve for change in position

• Solve for change in time

• Solve for initial position

• Solve for final position

Speed vs. Velocity•Are speed & velocity just two different words for the same thing?• In everyday life you probably use these words

interchangeably.

• In Physics class, speed and velocity are related, but NOT exactly the same.

Using The Speed Equation1. A car travels 30 meters in a trip that

lasts 2.0 seconds. What is the car’s speed?

2. If you go a distance of 45 meters at a speed of 16 m/s, how long does this trip last?

3. A fox runs at a speed of 9.7 m/s for 12 seconds. How far does the fox run?

How fast is fast?See if you can come up with an example of when an actual object might move at each speed.1) 0.1 m/s

About .22 mph, the tip of the second hand on your clock

2) 1 m/s 2.2 mph, a slow walk

3) 10 m/s 22 mph, a brisk bike riding speed

4) 100 m/s 220 mph, a supercar’s top driving speed

5) 1000 m/s 2,200 mph, about the F14 fighter jet’s top speed

• Distance is always positive.

• Time is always positive.

• Therefore, speed is always positive!• (Hint: Think about speed limit signs if you forget!)

Speed is scalar

So how do we tell the difference between moving backward and forward?

We need a new variable: velocity!

Velocity is defined as the change in position divided by the change in time.

Reminder: Δ means“change”

Velocity

A change in position, Δx, can be positive or negative.

That means that velocity can be positive or negative.

Velocity & Direction

•Positive Velocity implies the object is traveling: up/North or right/East

•Negative Velocity implies the object is traveling: down/South or left/West

-

+Up

Down

North

South+-

Left - Right

West - East

Velocity can have negative or positive values.

The sign of the velocity tells you the direction of motion.

Velocity is a vector (it will have a # value & a + or - sign)

Velocity is a vector

Using the Velocity Equation• A car starts at 30m and finishes

at 10m in a trip that takes 2.0 seconds.

• What is the change in position?

• What is the car’s velocity?

Using the Velocity Equation• A car travels at 15m/s. Four

seconds after starting out, it is at a position of 40m.

• What is the car’s change in position?

• Where did the car start from?

Finding Change in Position• Quick reminders:

• stands for position• Subscript “i” means “initial”• Subscript “f” means “final”

• Example: If a boy walks from a starting position of 3.2m to an ending position of 7.1, what is the boy’s change in position?

Finding Velocity• If a boy walks from a starting position of 3.2m to an

ending position of 7.1 in 2 seconds, what is his velocity?

Finding Velocity• If a boy walks from a starting position of 7.1m to an

ending position of 3.2m in 2 seconds, what is his velocity?

Positions & Velocities Part 1

+- 0

PositivepositionNegative

velocity

Can there be positive position and negative velocity?

NegativeVelocity

Positions & Velocity Part 2

+- 0

Positivevelocity

Negativeposition

Can there be negative position and positive velocity?

PositiveVelocity

Positions & Velocity Part 3

+- 0

NegativepositionNegative

velocity

Can there be negative position and negative velocity?

NegativeVelocity

Positions & Velocity Part 4

+- 0

Positiveposition

Positivevelocity

Can there be positive position and positive velocity?

PositiveVelocity

1. A swallow moves 80 meters east in 5 seconds. 0

What is its speed? V = 16 m/s

What is its velocity? = 16 m/s

How can the two be different? The velocity could be +16 m/s or -16 m/s

depending on the direction the bird travels

Homework

2. Write an English sentence that means the same as this equation:

Average velocity is equal to the change in position divided by the change in time.

Homework

+- 0

Positiveposition

Negativevelocity

Homework3. Give an example of an object with positive position and

negative velocity.

A person to the right of the origin but walking to the left would have a positive position and negative velocity.

NegativeVelocity

Homework4. Joel & Bryan are playing with a radar gun. When a car drives by the radar gun displays 65 mi/hr., Joel says that the value on the radar gun is a speed because there is no sign indicating direction. Bryan says you can’t assume that since the car was heading East which is a positive direction. Who is right? Explain.

5. How could we ultimately determine if the radar gun is displaying a speed or velocity?

Homework6. Convert each of the following. Show your work!

a. 22.1ft = _____________________ m

b. 3.1 hr = ______________________ s

c. 9.3m/s = _____________________ m/hr

d. 7.6 mi/s = _____________________ m/s

e. 76 mi/hr = ______________________ m/s