All quantities need to have the same dimensional units in a problem in order
for the solution to make sense. For example, if someone wanted to know how far
they go in 2 minutes if traveling 120 mi/hr, they would need to convert the 2 minutes
to 1/30 hr or convert 120 mi/hr to 2 mi/min. Without conversion, the result would
be 2 min times 120 mi/hr or 240 miles which doesn't make any sense. With conversion,
the result is 1/30 hr times 120 mi/hr, equal to 2 min times 2 mi/min, or 4 miles are
covered in 2 min at 120 mi/hr.
In this problem, the car's speed, given to be 60 mi/hr, and the car's acceleration, given to be -49090.9 mi/hr^{2}, both should to be converted to quantities involving feet (ft) and seconds (sec). Note that the acceleration is negative since the car is slowing down. The reason this needs to be done is that the car will be stopping in a matter of feet not miles and in a few seconds not hours. For example, 88 ft = 11/660 mi and so it is easier to work with the 88. It is certainly fine to do this problem in units of miles and hours, but then the quantity of 88 ft must be converted to miles. Conversion factors will be used to convert the car's speed and acceleration:
Simply multiply conversion factors so that the unwanted dimensional units (like hr and mi) cancel leaving the desired dimensional units (here, ft and sec):
Use a calculator to verify these calculations. Click on the calculator button, under tools to the left, for a calculator. So, a deceleration of 49090.9 mi/hr^{2} means that the car is accelerating at -20 ft/sec^{2}, where the acceleration is negative since the car is slowing down (decelerating). Next: Follow the "Deceleration Area" link to the left. |