Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

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 $\sqrt{2}$ times larger. (d) It is unchanged. (e) It becomes half as large.

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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:

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

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:

$\begin{array}{l} KE' = \frac{1}{2} m {(2 v)}^{2} \\ KE' = \frac{1}{2} m \times 4 v^{2} \\ KE' = 4 \times \frac{1}{2} {mv}^{2} \\ KE' = 4 \times KE \end{array}$

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.

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Physics For Scientists & Engineers

Answers without the blur.

Short Answer

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 $\sqrt{2}$ times larger. (d) It is unchanged. (e) It becomes half as large.

Step by Step Solution

Given information

Kinetic energy of a particle

Final kinetic energy

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Physics For Scientists & Engineers

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Short Answer

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 2 times larger. (d) It is unchanged. (e) It becomes half as large.

Step by Step Solution

Given information

Kinetic energy of a particle

Final kinetic energy

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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 $\sqrt{2}$ times larger. (d) It is unchanged. (e) It becomes half as large.