Q: A distance runner has just finished her race. During the first 3 kilometers, she ran with a constant speed of 5 meters per second. During the latter 7 kilometers, she ran with a constant speed of 14.4 kilometers per hour. What is her average speed for the race?
A: First, take note that the question asks for the runner’s average speed for the race as opposed to average velocity. Speed is a scalar quantity, so we must divide the total distance run by the total time transpired during the race. The total time that transpired isn’t given, so we must divide each leg of the race by the speed needed to traverse them. Before doing so, we must be sure that appropriate units are used throughout the problem solving process. The first speed is expressed in meters per second, so we begin by converting the associated distance into meters:
( 3 km )( 1 m / 10-3 km ) = 3,000 m
We may now determine how many seconds transpired over the first leg of the race:
[ 3,000 m / ( 5 m/s ) ] = 600 s
The second speed is expressed in kilometers per hour. Prior to dividing 7 km by the speed that is given, we must convert speed from kilometers per hour to kilometers per second:
( 14.4 km / hr )( 1 hr / 3,600 s ) = 4 x 10-3 km/s
[ 7 km / ( 4 x 10-3 km/s ) ] = 1,750 s
1,750 s + 600 s = 2,350 s
We now divide the total distance divided by the total time transpired:
Ooops!
If we want our answer to be expressed in the appropriate metric units, we must convert 10 km to its meter equivalent:
( 10 km )( 1 m / 10-3 km ) = 10-2 m
( 10-2 m / 2,350 s ) = 4.26 m/s
RENAISSANCE PHYSICS 