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