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Matter In Our Surroundings

Question
CBSEENSC9006343

The kinetic energy of an object of mass m moving with a velocity of 5 ms-1 is 25 J. What will be its kinetic energy when its velocity is doubled ? What will be its kinetic energy when its velocity is increased three times?

Solution

Given space that comma space

Initial space kinetic space energy space space equals space 25 space straight J

Now comma space we space know space that space kinetic space energy space is space directly space
proportional space to space the space square space of space velocity.
space
That space is comma
space
space space space space space space space space space space space space space straight E subscript straight k space proportional to space space straight v squared

therefore space space space space When space velocity space is space doubled comma space kinetic space energy space becomes comma

space space space space space space space space straight E subscript straight k space equals space left parenthesis 2 right parenthesis squared space cross times space Initial space straight K. straight E. space

space space space space space space space space space space space space space space equals space 4 space cross times space 25 space equals space 100 space straight J.

When space velocity space is space tripled comma space kinetic space energy space becomes comma

space space space space space space straight E subscript straight k space equals space left parenthesis 3 right parenthesis squared space cross times space Initial space straight K. straight E.

space space space space space space space space space space space equals space 9 space cross times space 25 space equals space 225 space straight J. space space space space space space space space space