D. Uniform
Motion
When
an object is moving at a constant speed (or velocity), the object
is traveling with uniform motion. The distance, D,
that the object will travel in time, T, depends
on the velocity, V. It is expressed mathematically
as
D = VT
If
we desire the distance in miles, we usually express the velocity
in miles per hour (mph) and time in hours. If the distance is
in kilometers, then the velocity would be in kilometers per hour
(kph).
Example 15
A biker travels 60 miles in 2.5
hours. Determine the biker's average speed.
Solution
The equation relating distance, velocity and time provides
60 = V(5/2)
Divide both sides by 5/2 to solve for V.
V = (60)2/5 = 24 miles/hour
Example 16
A car travels between two cities 400 miles apart in 7 hours.
The return trip takes 9 hours. Find the average speed of the
car.
Solution
The total distance is
2(400) = 800 miles. The total time is 7 + 9 = 16 hours. The average
speed is found from D = VT:
800 = V(16)
V = 800/16 = 50 miles/hour
Example 17
A police officer, traveling
at 100 miles per hour, pursues Philip who has a 30 minute head
start. The police officer overtakes Philip in two hours. Find
Philip's speed.
Solution
Let x miles per hour be Philip's speed. The distance traveled
by the officer equals the distance traveled by Philip:
2 × 100 = (2 + 30/60)x
200 = (2 + 0.5)x
200 = 2.5x therefore x = 80 mph
w E. Ratio and Proportion
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