A motorist driving at 25 meters/second decelerates to

15 meters/second. The combined mass of the vehicle and the driver is 1.5 * 10³ kilograms. What is the amount of mechanical work done by the vehicle?

Kinetic energy = (1/2) (mass) (speed) ²

Before slowing down, the car's speed is 25 m/s,

and its kinetic energy is ...

(1/2) (1,500 kg) (25 m/s) ²

= (1/2) (1,500 kg) (625 m²/s²)

= 468,750 joules.

After slowing down, the car's speed is 15 m/s,

and its kinetic energy is ...

(1/2) (1,500 kg) (15 m/s) ²

= (1/2) (1,500 kg) (225 m²/s²)

= 168,750 joules.

The car lost (468,750 - 168,750) = 300,000 joules of K. E.

The law of Conservation of Energy says:

That 300,000 joules had to go somewhere.

If it's a standard, gas-powered car, then the kinetic energy got

put into the brakes. The energy turned into heat, and the heat

was carried off in the air.

If it's a more modern electric or hybrid car, then the kinetic energy

spun the wheel motors, turning them temporarily into electrical

generators. The generators converted the kinetic energy into

electrical energy, which got put back into the car's batteries, and

could be used again. That's why electric cars use less gas.