Velocity
Name: __________________________________
Speed is how fast something moves.
Velocity is how fast something moves in a specific direction.
Per.: ____
In other words, velocity is speed in a specific direction. If you change speed or direction, you change velocity.
1. For each of the following examples, write “yes” or “no” in each box to show if each item changes.
Does it change? (yes / no)
Situation: A car …
rolls down a hill then across the flat ground.
position
(where it is)
speed
direction
velocity
Yes
Yes
Yes
Yes
drives north on Colby Ave. at a constant 20 mph
drives north on Colby, speeding up from 20 mph
to 30 mph
is stopped at a traffic light
drives around a curve at 40 mph
slows to a stop driving east
makes a lane change on the freeway at 60 mph
drives in a circle at a constant speed
Remember that speed is the rate of change in distance moved…
For velocity, we should say velocity is the rate of change in position.
We may not know the actual speed or velocity at a given moment in time, but we can easily calculate the average
speed or velocity knowing only the starting and ending points and times.
Average speed is the average distance traveled each unit of time.
 Speed adds all motion together.
o Think “How far did the car drive?” or “How much ground did the tires touch?”
Average velocity is the average change in position each unit of time.
 Velocity is concerned with results.
o Motion in opposite directions cancels out.
o Think “How far away from the starting point did the car end up?”
Example: You walk 100 meters North, then 50 meters South in a total of 2 minutes.
o Average speed = (100 + 50 meters walked) / (2 minutes) = (150 m) / (2 min) = 75 m/min
o Average velocity = (100 m – 50 m) / (2 minutes) = 50 m / 2 min = 0 m/min north
We calculate average velocity this way:
average velocity =
change in position d final  d initial d 2  d 1
d


 ..
 v avg
change in time
t final  t initial
t 2  t1
t
Wow, that’s a lot. . “∆” means “change in”. .
In many cases, d1 and t1 are zero, so we just have v = d / t
Stop, circle one ratio above that you understand, and let’s practice.
Solve the following problems.
Show your work! Remember to include direction when appropriate.
2. Ursula drives east on highway I-90 from milepost 30 to milepost 70 in 80 minutes.
a. What is her average speed?
Formula
a.
work
Answer with units
What is her average velocity? ________________________________
3. Dieter leaves home at 7:05 and walks 800. meters south on Colby to school, arriving at 7:25. What is his
average velocity?
Formula
work
Answer with units
4. A sales person drove 90 miles south from Everett to Olympia in 3.0 hours.
a. what was her average velocity?
Formula
work
Answer with units
b. How fast was she driving in Federal Way, half-way between the two cities?
(no calculations)
c. She drives back to Everett, arriving nine hours after she left. What was her average velocity for the
entire trip? Justify your answer.
(Hint: if you are calculating anything, you are doing it wrong.
Compare her starting and ending points, then look at the velocity equation.)
5. Calcuate the average velocity of the motion shown in each motion map. Calculate from the first to the last dot,
and assume a one second time interval between each pair of dots.
a.
0
Formula
1
2
3
4
5
6
7
8
work
9
meters
Answer with units
b.
0
Formula
2
work
4
6
8
10
12
14
16
18
meters
Answer with units
c.
0
Formula
Use the graph of
the dog Lucky’s
motion shown at
right to answer the
questions below:
5
10
15
20
25
30
35
40
45
work
cm
Answer with units
20
15
B
d (m)
A
C
10
5
5
6. Calculate Lucky’s average velocity in sections:
a. A
Formula
10
t (s)
15
20
25
work
Answer with units
work
Answer with units
work
Answer with units
Description of motion
b. B
Formula
Description of motion
c. C
Formula
Description of motion
d. A-B (5 through 15 seconds)
Formula
work
Answer with units
30
7. A hackey sack is kicked up (vertically) off the ground. It goes up 1.2 meters in 0.5 seconds, then hits the ground
1.0 seconds after it was kicked upwards.
a. What is its average velocity on the way up?
Formula
work
Answer with units
b. What is its average velocity on the way down?
Formula
work
Answer with units
c. What is its average velocity for the entire time it is in the air?
Formula
work
Answer with units
8. Make up your own example. Include a word problem, a graph or motion map showing the motion in the word
problem, and a solution.