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Question

A car is accelerated on a road and it attains a velocity 3 times of the initial velocity. In this process the kinetic energy of the car

A
does not change.
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B
becomes 3 times that of the initial.
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C
becomes 9 times that of the initial.
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D
becomes 27 times that of the initial.
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Solution

The correct option is C becomes 9 times that of the initial.
Let the mass of the car be m and its initial speed be u and final speed be v.

From the data given in the question, Car is accelerated and final velocity of car is 3 times its initial velocity.., i.e v=3u ........(1)

From the definition of kinetic energy,

Initial kinetic energy of car , Ki=12mu2

Final kinetic energy of car , Kf=12mv2

Substituting (1) in the above equation we get,

Kf=12m×(3u)2=9×(12mu2)

Kf=9×Ki

Hence, option (c) is the correct answer.
Note: Acceleration (a) is the rate of change of velocity of an object.
a=dvdt

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