A car weighing 1000kg and travelling at 30m/s stops at a distance of 50m decelerating uniformly. What is the force exerted on it by the brakes? What is the work done by the brakes? In this question, force applied by brakes is found to be negetive but the work done is still positive. How?

Mass of the car, m = 1000 kg

Initial speed, u = 30 m/s

Distance traveled, s = 50 m

Final speed, v = 0

Acceleration = a

Using,

v² = u² + 2as

=> 0 = 30² + 2a(50)

=> a = -9 m/s²

Thus, deceleration is = 9 m/s²

Now,

Force applied by brakes = ma =(1000)(-9) = -9000 N

Negative sign implies the brakes opposes the motion.

Work done by the brakes = (-9000)(50) = -450000 J

The work done by brakes is negative as the force by brakes opposes the motion, hence, displacement 50 m and force are oppositely directed.