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Expert-verified Found in: Page 177 ### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271 # If the speed of a particle is doubled, what happens to its kinetic energy? (a) It becomes four times larger. (b) It becomes two times larger. (c) It becomes $\sqrt{\mathbf{2}}$ times larger. (d) It is unchanged. (e) It becomes half as large.

The correct option is (a): it becomes four times larger.

See the step by step solution

## Given information

The mass of the particle is m.

The initial speed of a particle is v.

The final speed of the particle is 2v.

## Kinetic energy of a particle

The formula for the initial kinetic energy of the particle is given by the following:

${\mathbf{KE}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}$

So, if the particle’s mass is higher and it travels faster, the magnitude of the kinetic energy of the particle is also higher; otherwise, it is lower.

## Final kinetic energy

According to the question, after the speed of a particle is doubled, the value of the final kinetic energy of the particle is given by the following:

$\begin{array}{l}\mathrm{KE}\text{'}=\frac{1}{2}\mathrm{m}{\left(2\mathrm{v}\right)}^{2}\\ \mathrm{KE}\text{'}=\frac{1}{2}\mathrm{m}×4{\mathrm{v}}^{2}\\ \mathrm{KE}\text{'}=4×\frac{1}{2}{\mathrm{mv}}^{2}\\ \mathrm{KE}\text{'}=4×\mathrm{KE}\end{array}$

From the above expression, if the speed of a particle is doubled, its kinetic energy becomes four times larger.

Hence, the correct option is (a): it becomes four times larger. ### Want to see more solutions like these? 