- #1

- 40

- 0

## Homework Statement

The driver of a car at 31 m/s sees (t = 0, x = 0) an obstacle down the road and brakes. The car slows down with a constant deceleration which has a magnitude of 6 m/s^2. Select the correct statement below (let d = stopping distance, all units are SI)

a. The position x(t) = 31t + 3t^2

b. The velocity v(t) = 31 - 3t

c. Stopping distance = 961 - 12d

d. The velocity v(t) = d/t

e. None of the above

## Homework Equations

Vf = Vi + at

Vf^2 = Vi^2 + 2ad

Xf = Xi + Vi*t + .5at^2

## The Attempt at a Solution

a. The position x(t) = 31t + 3t^2

is not correct, because Xf = Xi + Vi*t + .5at^2, so x(t) = 31t - 3t^2

b. The velocity v(t) = 31 - 3t

is not correct, because Vf = Vi + at, so v(t) = 31 - 6t

c. Stopping distance = 961 - 12d

is correct, because Vf^2 = Vi^2 + 2ad, so 0 = 31^2 + 2(-6)d = 961 - 12d => d = 80 m

d. The velocity v(t) = d/t

is correct, because the velocity at time t can solved by dividing the distance traveled over the time taken

But the answer key says c. is correct, why is d. not also correct? Is it because dividing d/t would only give the AVERAGE velocity, not the velocity at time t?

Thanks,

Coop