Analytical Solution


In this final step, the solution to the given problem will be determined analytically.

It is given that the deceleration is 20 ft/sec, so the acceleration as a funtion of time is

a(t) = -20.

Integrate a(t) to find that the car's speed as a function of time is
v(t) = -20t + v0.

It is given that v(0) = 88 so
88 = -20*0 + v0.

So, v0 = 88, and the car's speed as a function of time is
v(t) = -20t + 88.

Integrate v(t) to find the car's distance as a function of time
d(t) = -10t2 + 88t + d0.

It can be taken that d(0) = 0, so d0 = 0 and the car's distance as a function of time is
d(t) = -10t2 + 88t.

How close is your answer?


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