A Car Brakes with a Constant Deceleration:: Find Initial Velocity :: Applications of Antiderivatives

A Car Brakes with a Constant Deceleration of 16 ft/s^2, producing skid marks 200 ft long before coming to a stop. How fast was the car traveling when the brakes were first applied?

This problem is a good application of antiderivatives.

We have a(t) = -16 since it acts opposite to the direction of positive displacement.

v(t) = ∫a(t) dt = -16t+v0
s(t) = ∫v(t) dt = -8t^2+v0t + s0

We find the time ts when the cars stops and use this to compute the velocity the cars was at when the brakes were applied.

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