Question

A car moving 20 m/s in the positive x-direction slams on the brakes and stops after skidding 20 m. what was its acceleration during this period?

Answer 1

To find the acceleration of the car, we can use the following relationship:
$v_f^2 - v_i^2 = 2 aS$
where
$v_f=0$ is the final speed of the car (it is zero because the car comes to rest)
$v_i=20 m/s$ is the initial speed of the car
$a$ is the acceleration
$S=20 m$ is the distance covered

By rearranging the equation, we get:
$a= \frac{-v_i^2}{2 S}= \frac{-(20 m/s)^2}{2 (20 m)} =-10 m/s^2$
where the negative sign means it is a deceleration.