# Differential Equations

A car is traveling at 70 mph skids 240 ft after it's breaks are suddenly applied. Assuming that the cars breaking system provides a constant deceleration, find that deceleration. How long did it take the car to stop?

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1. You want me to do this with calculus with these terrible units evidently so I will.
70 mph (1h/3600s)(5280ft/m) = 103 ft/s

d^2x/dt^2 = a
dx/dt = a t + Vi where Vi is initial speed
x = (1/2) a t^2 + Vi t + Xo wher Xo is initial x (call it 0 here
so
dx/dt at end = 0
0 = a t + 70 so a = -103/t
then
240 ft = (1/2) at^2 + 103 t
240 = (1/2)(-103/t) t^2 + 103 t
240 = -51.5 t + 103 t = 51.5 t
t = 4.66 seconds to stop
a = -103/4.66 = -22.1 ft/s^2
240 =

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