Kinetic Energy

The kinetic energy is given by: Thus, the energy to accelerate the car from to is proportional to , and the energy required to accelerate from to is three times as great. Therefore, the energy is three times as great.

The work done by a variable force is given by the integral: Substitute and integrate from to : Evaluating the integral: Hence, the correct answer is (c).

When a hydrogen atom transitions from a lower energy state to a higher energy state, its potential energy (PE) increases because it is farther from the nucleus. However, the kinetic energy (KE) decreases because the atom is in a higher energy state and the electron moves more slowly as the energy levels increase. Hence, the correct answer is (c).