Let the speed of the cart and the time be
v and t respectively.
Since the speed is a positive value, the speed with respect
to time is a one-to-one function as shown in the diagram on the left.
Rearranging the function in terms of v gives
t = v3/2/2500
When the speed is 10 mile/hour, the time is
t = 103/2/2500 = 0.0126 hour = 30.36 s