5) c I don\'t quite understand how one gets those answers. 4. An object of mass

Question

5) c

I don't quite understand how one gets those answers.

4. An object of mass m moves with a velocity v. If the kinetic energy of the mass is doubled, then the magnitude of its velocity must have increased by a factor of a. root 2 b. 2 c. 4 d. 8 e. None of the above 5. An object of mass m moves is attached to a spring which is stretched a distance d. If the amount the spring is stretched is increased to 2d, then the amount of potential energy stored in the spring increases by a factor of a. root 2 b. 2 c. 4 d. 8 e. None of the above

Explanation / Answer

(4) Kinetic energy = KE = 0.5 m v^2

If the new kinetic energy = 2 KE = 2 * 0.5 m * v^2 = 0.5 m u^2

u = sqrt(2) v

Hence answer is Option a

(5) Potential Energy stored = 0.5 k d^2

New stretching = 2 d

New Potential Energy = 0.5 * k * (2d)^2 = 2 k d^2

Factor = 2 / 0.5 = 4

Hence answer is Option c

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