A car of mass 1000 kg is travelling down a steep hill. The brakes fail and the driver uses a horizontal sand-filled safety road to stop the car.

The car enters the sand at a speed of 10m / s and experiences a constant stopping force of 2500 Ν.

How far does the car travel in the sand before coming to rest?

There are two methods we can use to find the distance traveled. One method is the work-energy theorem, which says the work done by the stopping force is equal to the car's change in kinetic energy. Another method is to use Newton's second law of motion to find the acceleration, then use a kinematic equation to solve for the distance.

Using the work energy theorem, work (W) is equal to the change in kinetic energy (KE). Work is equal to force (F) times distance (d), and kinetic energy is half the mass (m) times the square of the speed (v).

W = ΔKE

Fd = ½ mv²

(2500 N) d = ½ (1000 kg) (10 m/s)²

d = 20 m

Alternatively, using Newton's second law of motion, the net force (F) is equal to the mass (m) times the acceleration (a).

F = ma

-2500 N = (1000 kg) a

a = -2.5 m/s²

Use a kinematic equation, also known as a SUVAT equation.

v² = u² + 2as

(0 m/s)² = (10 m/s)² + 2 (-2.5 m/s²) d

d = 20 m