Answer: 12.5 seconds
Explanation:
To find out how many seconds after the driver applies the brakes the car comes to a stop, we need to find the value of t when the car's velocity, s'(t), is equal to 0. The velocity of the car is the derivative of the position function, so we can find it by differentiating s(t).
s(t) = 50t - 2t^2
s'(t) = 50 - 4t
To find when the velocity is 0, we set s'(t) = 0 and solve for t:
0 = 50 - 4t
4t = 50
t = 50/4
t = 12.5 seconds
Therefore, it takes the car 12.5 seconds to come to a stop after the driver applies the brakes.