Question

The chemical potential energy in gasoline is converted to kinetic energy in cars. If a car accelerates from zero to 60 km/h, compared to the energy necessary to increase the velocity of the car from 30 to 60 km/h, the energy necessary to increase the velocity of the car from 30 to 60 km/h is:

• A. half as great
• B. the same
• C. twice as great
• D. three times as great

Hint:

Kinetic energy increases with the square of the velocity. The energy required to increase velocity from 30 to 60 km/h is greater than from 0 to 30 km/h.

Answer 1

The Correct Option is D

The kinetic energy $K$ is given by: \[ K = \frac{1}{2} m v^2 \] Thus, the energy to accelerate the car from $0$ to $60 \, \text{km/h}$ is proportional to $v^2$, and the energy required to accelerate from $30 \, \text{km/h}$ to $60 \, \text{km/h}$ is three times as great. Therefore, the energy is three times as great.