Suppose that a car starts from rest with its engine providing a constant acceler

Question

Suppose that a car starts from rest with its engine providing a constant acceleration of 13.5 ft/s^2. If air resistance provides (.0006)v^2 ft/s^2 of deceleration, find the following,

a) The cars maximum possible (limiting) velocity

b)How long the car takes to attain 90% of its limiting velocity

c) How far it travels in doing so.

Please show me detailed work, i have looked at similar problems but the V^2 in the air resitance is what is making the integration tricky. the answer to part b is 16.36, although I cant seem to get there.

Explanation / Answer

dv/dt = 13.5-0.0006v^2

so maximum velocity

0 = 13.5-0.0006v^2

v = 150ft/s

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