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Q11 OQ

Expert-verifiedFound in: Page 177

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.

The mass of the particle is m.

The initial speed of a particle is v.

The final speed of the particle is 2v.

**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.

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:

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

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.

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