Let's practice some conversions. A speed of miles per hour equals a speed of feet per second, and a speed feet per second equals a speed of miles per hour. Recall that there are 5280 feet in a mile, and 3600 seconds in an hour. Recall that velocity is the derivative of distance, and acceleration is the derivative of velocity. Suppose that acceleration is constant, and equal to . Suppose at time 0 your velocity is .

Let denote your velocity at time . Then

. Suppose at time your distance (in whatever direction you are moving) is D.

Let denote your distance at time . Then


Let's translate that into a familiar context. Suppose feet per second squared, is you height at time , is your initial height, and is your initial velocity. Then your height at time is , your velocity at time is , and your acceleration at time(t) is, of course, feet per second squared.

You can earn partial credit on this problem.