Question

The driver of a car slams on the brakes, causing the car to slow down at a rate of 17ft/s2 as the car skids 285ft to a stop.
How long does the car take to stop?
What was the car's initial speed?

Answer 1

1) 5.79 s

2) 98.4 ft/s

Explanation:

1)

The motion of the car is a uniformly accelerated motion (it means it travels with constant acceleration), so we can find the time it takes for the car to stop by using the following suvat equation:

$s=vt-\frac{1}{2}at^2$

where

s is the distance travelled

v is the final velocity

t is the time

a is the acceleration of the car

In this problem we have:

s = 285 ft is the distance travelled

$a=-17 ft/s^2$ is the acceleration of the car (negative since the car is slowing down)

v = 0 ft/s is the final velocity of the car, since it comes to a stop

Solving for t, we find:

$t=\sqrt{\frac{-2s}{a}}=\sqrt{\frac{-2(285)}{-17}}=5.79 s$

2)

The initial speed of the car can be found by using another suvat equation, namely:

$v=u+at$

where

v is the final speed

u is the initial speed

a is the acceleration

t is the time

In this problem, we have:

v = 0 is the final speed of the car

$a=-17 ft/s^2$ is the acceleration of the car (negative since the car is slowing down)

t = 5.79 s is the total time of motion (found in part 1)

Therefore, the initial speed of the car is:

$u=v-at=0-(-17)(5.79)=98.4 ft/s$