Question

In case one, a car speeds up from zero m/s to 15 m/s. In case two, the same car speeds up from 15 m/s to 30 m/s. The mass of the car is 1000 kg. Compare the energy needed to provide the increase in speed in each case. Give your answers in joules. (a) In case one, how much energy is needed? J (b) In case two, how much energy is needed? J (

c) In case two, how many more times the energy was needed than in case one?

Three times as much energy was needed.

Twice as much energy was needed.

The same amount of energy was needed in both cases.

Four times as much energy was needed.

Answer 1

Using the kinetic energy equation

KE = 0.5*m*v²

(A)

Original energy = 0.5 * (1,000 kg) * (0.0 m/s)² = 0 J
Final energy = 0.5 * (1,000 kg ) * (15 m/s)² = 112500 J

Difference = 112500 J

(B)

Original energy = 0.5 * (1,000 kg) * (15 m/s)² = 112500 J
Final energy = 0.5 * (1,000 kg) * (30 m/s)² = 450000 J

Difference = 337500 J

(C) (337500 J) / (112500 J) = 3x, so

It takes 3x more energy in the second stage than the first