The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 50t - 2t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?

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To find the number of seconds it takes for the car to come to a stop, we need to determine when the car's velocity reaches zero.

The velocity of the car, v(t), can be found by taking the derivative of the position function, s(t), with respect to time, t.

v(t) = s'(t) = d/dt(50t - 2t^2)

To find when the car comes to a stop, we set v(t) equal to zero and solve for t:

0 = 50 - 4t

Solving this equation for t will give us the number of seconds it takes for the car to come to a stop.

0 = 50 - 4t
4t = 50
t = 50/4
t = 12.5

Therefore, the car comes to a stop 12.5 seconds after the driver applies the brakes.