Distance, Velocity, Acceleration, and Rectilinear

Question

The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t - 3t², t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?

Options:

1. 60 sec
2. 20 sec
3. 30 sec
4. 10 sec

Answer 1

We are given the position function, and we are asked when the velocity is equal to 0.

To get the velocity function, we take the derivative of the position function s(t) = 60t - 3t².

Using the power rule on both terms, we get

s'(t) = 60 - 6t

This is the velocity of the car at time t. To find out when it is stopped, we set the function equal to 0, and solve for t.

0 = 60 - 6t

6t = 60

t = 10