Question

if the velocity of the object is doubled how much will its kinetic energy

Answer 1

mass of object = m

Let initial velocity of object = v

$ke = \frac{1}{2} m {v}^{2}$

if velocity is doubled,

new velocity = 2v


$new \: ke = \frac{1}{2} m {(2v)}^{2} = \frac{1}{2} m \times {4v}^{2}$

$new \: ke = 4 \times \frac{1}{2} m {v}^{2} = 4 \times ke$

Thus the kinetic energy will be 4 times if the velocity is doubled.

Answer 2

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mass of object = m

Let initial velocity of object = v

$ke = \frac{1}{2} m {v}^{2}$

if velocity is doubled,

new velocity = 2v

$new \: ke = \frac{1}{2} m {(2v)}^{2} = \frac{1}{2} m \times {4v}^{2}$

$new \: ke = 4 \times \frac{1}{2} m {v}^{2} = 4 \times ke$

Thus the kinetic energy will be 4 times if the velocity is doubled.