   Chapter 5, Problem 17CQ

Chapter
Section
Textbook Problem

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.

To determine
The kinetic energy of the particle if the speed of the particle is doubled.

Explanation

Given Info:

The speed of the particle is doubled.

Formula to calculate the kinetic energy of the particle is,

KE=12mv2

• v is the velocity of the particle
• m is the mass of the particle

Since, the speed of the particle is doubled; the kinetic energy of the particle is

KE=12m(2v)2=4(12mv2)

Thus, when the speed of the particle is doubled, the kinetic energy of the particle becomes four times larger.

Conclusion:

Since, the kinetic energy of the particle is directly proportional to the square of the speed of the particle; when the speed of the particle is doubled, the kinetic energy of the particle becomes four times larger

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