Name:____________- _____________
Date: ___________
Science 10: Unit 8.2 – Average Velocity
SPEED AND VELOCITY, WHAT’S THE DIFFERENCE?
Velocity is a ________________ – has direction and magnitude. Speed is a scalar, it only has _________________.
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 ____________________________________________________________________________
Speed can be called the _____________________________________________________________________________
AVERAGE VELOCITY:
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).
In a way, average velocity is a simplification. It tells us _____________________________________________________
_______________________ It does not tell us exactly what velocity the object moved at for all instants in that interval.
Calculating Average Velocity: The relationship between average velocity, displacement and time is given by:
1. What is the average velocity of a dog that takes 4.0 s to run forward 14 m?
2. A boat travels 280 m east in a time of 120 s. What is the boat’s average velocity?
Calculating Displacement: The relationship between displacement, average velocity, and time is given by:
1. What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s?
2. A person, originally at the starting line, runs west at 6.5 m/s.
What is the runner’s displacement after 12 s?
Calculating Time: The relationship between time, average velocity, and displacement is given by:
1. How long would it take a cat walking north at 0.80 m/s to travel 12 m north?
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?
CONVERTING UNITS: m/s <-> km/h
Example: Using unit analysis, convert 75km/h to m/s.
1. Convert 95 km/h to 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?
3. What is the displacement of an airplane flying 480 km/h [E] during a 5.0 min time interval?
SOLVING PROBLEMS WITH VELOCITY, DISPLACEMENT AND TIME:
Problem #1: What is the average velocity of a skateboard that is goes 50 m [W] over a time interval of 8 seconds?
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?
Problem #3: A deer is running forward at a speed of 46 km / h. How far does it travel in 30 seconds?
Problem #4: How many minutes would it take a car moving at an average velocity of 82 km / h to travel 125 km?
Chapter 8.1 Practice Exercises
1. Karen was snowboarding down a mountain. She started at 200 m north of a sign, and rode to a point that was 500 m south
of the sign. Calculate her displacement.
2. John rode his bicycle from point that was 3 km west of a point and stopped at a place located 12 km east of that point.
Calculate his displacement.
3. Sara’s displacement was calculated to be 2,000 km [W]. If she started at a point that is 7,000 km east of home, what was
her final position?
When drawing vector diagrams, we use an arrow to show both the magnitude (amount of speed or distance) and also the
direction of the movement.
4. Paul left his home, and walked due north at 3 m/sec for 2 minutes. He then stopped to talk to his uncle on the street corner
for 6 minutes. He then walked due west for 5 minutes, moving at 4 m/sec. Then he went due south for 2 minutes, moving
at 3.5 m/sec. He then walked due east for 4 minutes, travelling the last 1120 m to his friend’s house.
a.
b.
c.
d.
e.
f.
Draw a vector diagram, using a scale of 1 cm = 100 m
Find the total distance traveled by Paul.
How long did it take him to make the trip, including his conversation time?
What is the time interval from when he met his uncle, to when he arrived at his friend’s house?
If we don’t include the time he spent talking to his uncle, what is Paul’s average speed? (2 decimal places)
What is the position of Paul’s friend’s house, relative to his own house?
A position-time graph shows how an objects position changes over time, with time on the horizontal axis, and position on the
vertical axis. Uniform (unchanging) motion is shown as a straight line. A best-fit line is drawn through as many data points as
possible to show the pattern. We can also use interpolation or extrapolation for points not given.
5. For the first 20 seconds, Michelle walks at a constant speed until she gets to a point that is 50 m to the right of her house.
She stands there for 10 seconds, then over the next 30 seconds, moves at a constant speed to a point that is 20 m to the left of
her house. She returns to her home in 40 seconds, moving at a constant speed. Create a position-time graph, and label both
axis. When did her fastest speed occur?
Chapter 8.2 Practice Exercises
Answer the following questions on a separate piece of paper. Show all formulae and calculations!
1. If a football flies through the air at 12 m / s, what would its displacement be after 3 s?
2. Mike drives his motorcycle a distance of 600 km, moving at an average velocity of 85 km /h. How many hours does
this trip take him?
3. If a student is running at 4.3 m / s, what is their velocity in km / h?
4. If an airplane is flying at 740 km / h, what is the velocity in m / s?
5. A hang glider’s displacement is 28 km [S] after flying for 45 minutes. What is its average velocity in km/h and m/s?
6. What is the displacement of a truck that has an average velocity of 56 km / h over a time interval of 120 seconds?