Let's practice some conversions. A speed of $m$ miles per hour equals a speed of feet per second, and a speed $f$ 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 $A$. Suppose at time 0 your velocity is $V$.

Let $v(t)$ denote your velocity at time $t$. Then

$v(t) =$ . Suppose at time $t=0$ your distance (in whatever direction you are moving) is D.

Let $d(t)$ denote your distance at time $t$. Then

$d(t) =$ .

Let's translate that into a familiar context. Suppose $A=-32$ feet per second squared, $h(t)$ is you height at time $t$, $H$ is your initial height, and $V$ is your initial velocity. Then your height $h(t)$ at time $t$ is $h(t) =$ , your velocity at time $t$ is $v(t) = h'(t) =$ , and your acceleration at time(t) is, of course, $a(t) = v'(t) = h''(t) =$ feet per second squared.

You can earn partial credit on this problem.