The qualifying time for the race is set at 37.895 seconds. if the track is 2.5 miles, how many feet per seconds was the driver going? . and how many miles per hour?
(5280 feet in 1 mile).

Step-by-step explanation:

There are two parts to this problem:

As you can learn from any speed limit sign, speed is in units of distance per time--miles per hour in the US. To compute speed, you divide distance by time.

If we were to use the given numbers directly, dividing distance in miles by time in seconds, our speed would have units of miles per second. In order to change the units to the ones asked for by the problem statement, we need to make one of two conversions.

For the first part, we need to convert miles to feet, so our speed is in feet per second instead of miles per second. For the second part, we need to convert seconds to hours, so the speed is in miles per hour.

__

Any units conversion can be done using a conversion factor that is a fraction that has a value of 1. That is, its numerator is equal to its denominator.

For the conversion from miles to feet, we want to cancel units of miles and leave units of feet. The operation on units looks like ...

The units of miles in the numerator cancel the units of miles in the denominator, so we're left with feet per second, as we want. In order to make the conversion factor have a value of 1, it must be ...

  (5280 ft)/(1 mi) . . . . . . numerator equal to denominator

(a) Express the speed in ft/s:

(2.5 mi)/(37.895 s) × (5280 ft)/(1 mi) = 2.5·5280/37.895 ft/s ≈ 348.331 ft/s

__

(b) For the conversion to miles per hour from miles per second, we need to cancel the units of seconds in the denominator and replace them with hours. The conversion factor for that is ...

  (3600 s)/(1 h) . . . . . . numerator equal to denominator

(2.5 mi)/(37.895 s) × (3600 s)/(1 h) = 2.5·3600/37.895 mi/h ≈ 237.498 mi/h