Question

Speed
Speed is a measure of how fast something is moving. It is calculated
by dividing the distance an object moves by the amount of time it
takes the object to move that distance. For example, a car that travels
50 kilometers in one hour has a speed of 50 km/h. In other words,
speed is a ratio of distance to time.
Many objects do not move at a constant speed. For example, a car
traveling at a speed of 50 km/h may slow down as it approaches a
red light and then speed up again when the light turns green. The
car’s speed at any given moment in time is called its instantaneous
speed.
Average Speed
Although an object may not have a constant speed, its motion over a
given distance can be expressed as its average speed. Average speed
is the total distance traveled, divided by the total time it takes to
travel that distance. The equation for average speed is:
Average speed
, or
For example, if a car travels 80 kilometers in the first hour of a two-
hour trip and 100 kilometers in the second hour, its average speed for
the total trip would be:

90 km/hr
The equation for average speed can be rewritten to find either the
total time or the total distance when the other two variables are
known:
t
and d
v
t
d
v
180 km
2 h
(80 km 1 100 km)
(1 h 1 1 h)
v
d
t
v
Total distance
Total time

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Section 11.2 Speed and Velocity
Solved Examples
Example 1:
A winner of the Indianapolis 500 auto race completed
the 806.5-kilometer race in 2.98 hours. What was the
driver’s average speed during the race?
Given: Total distance (d)
806.5 km
Total time (t)
2.98 h
Unknown: Average speed ( )
Equation:
Solution:
270.6 km/h
Example 2:
Different animal species show a tremendous range of
variation in their speed of movement. The fastest land
animal, the cheetah, can travel 100.0 km/h. In contrast,
the slowest animal, a species of sea crab, has an average
speed of just 5.7 km/y. How long would it take the sea
crab to travel 100.0 km?
Given: Average speed ( )
5.7 km/y
Total distance (d)
100 km
Unknown: Total time (t)
Equation: t
Solution: t
17.5 y
Example 3:
You usually see lightning before you hear thunder,
because light travels faster than sound. Juan saw a flash
of lightning and heard the thunder 6 seconds later.
Sound travels at a speed of 340 m/s in air. How far
away was Juan from the lightning?
Given: Average speed ( )
340m/s
Total time (t)
6 s
Unknown: Total distance (d)
Equation: d
t
Solution: d
(340 m/s)
(6 s)
2,040 m
v
v
100 km
5.7 km>y
d
v
v
806.5 km
2.98 h
v
d
t
v
v
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ved.
Practice Exercises
Exercise 1:
In a boat race, Dan drove his motorboat over the
1000-meter course from start to finish in 40 seconds.
What was Dan’s average speed during the race?
Exercise 2:
It takes Serina 0.25 hour to drive to school. Her route is
16 km long. What is Serina’s average speed on her drive
to school?
Exercise 3:
In a competition, an athlete threw a flying disk
139 meters through the air. While in flight, the disk
traveled at an average speed of 13.0 m/s. How long
did the disk remain in flight?
Exercise 4:
If you shout into Grand Canyon, your voice travels at
the speed of sound (340 m/s) to the bottom of the
canyon and back, and you hear an echo. How deep is
the Grand Canyon in a spot where you can hear your
echo 5.2 seconds after you shout?
Exercise 5:
Sound travels much faster in water than air. It takes
4.2 seconds for the sound of an explosion to travel
underwater to a diver 6,006 m away. What is the speed
of sound in water?
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Answer 1

Here are the solutions to Exercises 1–5.

1) Given: d = 1000 m, t = 40 s.
v = d / t = 1000 ÷ 40 = 25 m/s.

2) Given: d = 16 km, t = 0.25 h.
v = d / t = 16 ÷ 0.25 = 64 km/h.

3) Given: d = 139 m, v = 13.0 m/s.
t = d / v = 139 ÷ 13.0 ≈ 10.7 s.

4) Given: round-trip time = 5.2 s, speed of sound = 340 m/s. One-way time = 5.2 / 2 = 2.6 s.
depth = v × t(one-way) = 340 × 2.6 = 884 m (≈ 8.84×10^2 m).

5) Given: d = 6006 m, t = 4.2 s.
v = d / t = 6006 ÷ 4.2 = 1430 m/s (≈ 1.43×10^3 m/s).