If the speed of your car is doubled, how does its $KE$ (kinetic energy) change?

• A. The $KE$ decreases by half.
• B. The $KE$ remains the same.
• C. The $KE$ increases by a factor of $4$.
• D. The $KE$ doubles.

Answer: (C)

Verified step by step guidance

1. Recall the formula for kinetic energy: \(\text{KE} = \frac{1}{2} m v^{2}\), where \(m\) is the mass of the car and \(v\) is its speed.
2. Identify the initial kinetic energy as \(\text{KE}_1 = \frac{1}{2} m v^{2}\).
3. When the speed is doubled, the new speed becomes \$2v\(. Substitute this into the kinetic energy formula to get the new kinetic energy: \)\text{KE}_2 = \frac{1}{2} m (2v)^{2}$.
4. Simplify the expression for \(\text{KE}_2\): \(\text{KE}_2 = \frac{1}{2} m \times 4v^{2} = 4 \times \frac{1}{2} m v^{2} = 4 \times \text{KE}_1\).
5. Conclude that doubling the speed results in the kinetic energy increasing by a factor of 4.