Question

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The kinetic energy of an object of mass M moving with a velocity of 5 M per second is 25 Joule. what will be its kinetic energy when its velocity is doubled ??what will be its kinetic energy when its velocity is increased 3 times

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Answer 1

First of all, calculate mass "m" of the object.

Now, Kinetic energy = $\frac{1}{2}$m$v^{2}$

25=$\frac{1}{2}$ × m × $5^{2}$

25 = $\frac{1}{2}$ × m × 25

m = $\frac{25*2}{25}$

= 2 kg

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(i) In first case, the velocity of 5 m $s^{-1}$ is doubled, so the velocity becomes 5 × 2 = 10 m $s^{-1}$

Kinetic energy = $\frac{1}{2}$m$v^{2}$

= $\frac{1}{2}$ × 2 × ( $10^{2}$ )

= $\frac{1}{2}$ × 2 × 100

= 100J

Thus when velocity of object is doubled, its kinetic energy becomes 100J

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(ii) In the second case, the velocity of 5 m $s^{-1}$ is increased three times so the velocity becomes 5 × 3 = 15 m $s^{-1}$

Kinetic energy =  $\frac{1}{2}$m$v^{2}$

= $\frac{1}{2}$ × 2 × $15^{2}$

=$\frac{1}{2}$ × 2 × 225

= 225J

Hence when velocity of object is increased 3 times, kinetic energy becomes 225J

Hope Helped :)

Answer 2

Let the mass be m

v = 5m/s

K.E = 25 J

K.E = 1/2 mv^2

25 = 1/2 m (5)^2

25 x 2 = 25m

m = 2 kg

Now if the velocity becomes 3 times then the velocity is 3 x 5 = 15m/S

Now new K.E = 1/2 x 2 x 15^2

= 225 J