At time t = 0 a car has a velocity of 16 m/s.It slows down with an acceleration given by a = -0.50t, in m/s² for t in seconds.By the time it stops it has traveled: A)15 m B)31 m C)62 m D)85 m E)100 m

Question

Quizplus · Accepted Answer

The velocity of the car can be represented as the integral of the acceleration with respect to time:

v(t) = -0.25t^2 + C

We know that at t = 0, v(0) = 16, so we can solve for C:

16 = -0.25 (0) ^ 2 + C

C = 16

So the velocity of the car is:

v(t) = -0.25t^2 + 16

To find the distance traveled, we can integrate the velocity with respect to time:

s(t) = -0.083t^3 + 16t + D

We don't know what D is, but we do know that when the car stops, its velocity is 0. So:

0 = -0.25t^2 + 16

t = 8

Plugging this into our equation for s(t):

s(8) = -0.083(8)^3 + 16(8) + D

s(8) = 85 + D

So the car has traveled 85 meters when it stops. Therefore, the answer is (D).

At Time T = 0 a Car Has a Velocity