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Expert-verified Found in: Page 138 ### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922 ## When the speed of your car is doubled, by what factor does its kinetic energy increase?

(a) $$\sqrt 2$$. (b) 2. (c) 4. (d) 8.

The correct answer is option (C).

When the speed of the car is doubled, the kinetic energy increases by a factor of 4.

See the step by step solution

## Step 1: Characteristics of kinetic energy

The kinetic energy of a particle relies on the mass as well as the speed of the particle. It is directly proportional to the square of the speed. In the standard international system, kinetic energy is measured in terms of Joule (J).

The formula for the kinetic energy of the car is given by:

\begin{aligned}KE = \frac{1}{2}m{v^2}\\KE \propto {v^2}\end{aligned}

Here, m is the mass of the car, and v is the speed of the car.

## Step 2: Increase in kinetic energy of the car

From the formula of kinetic energy, it is evident that the kinetic energy is affected by the car's speed, which means that it increases with an increase in kinetic energy. When the speed of the car is doubled, the kinetic energy will get quadrupled as it varies with the second power of speed.

Thus, option (c) is the correct answer. ### Want to see more solutions like these? 