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## Homework Statement

A car traveling 70mph can stop in 157ft. What is its rate of acceleration? (assume its constant)

## The Attempt at a Solution

70mph=102.6ft/sec

So if the the acceleration is constant, the graph of velocity will be a line with constant slope. The integral then will be the area of the triangle with heigh 102.6 and width t, the time when velocity=0. We also know that the integral is equal to 157. So, we have 102.6/2*t=157

t=3.05 seconds

Since acceleration is distance/second/second we multiple 102.6*3.05 seconds which is 312.9 and this should be the rate of acceleration. However if I were to use differential equations to create a position function and evaluate it at t=3.05 I don't get 157ft which suggests that I did something wrong. So, what am I doing wrong? Thanks for the help.