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

Explanation

First of all we calculate the mass 'm' of the object.
Now, Kinetic energy `= (1)/(2)mv^(2)`
So, `25 = (1)/(2) xx m xx (5)^(2)`
`25 = (1)/(2) xx m xx 25`
`m = (25 xx 2)/(25)`
So, Mass, m = 2 kg
(i) In this first case, the velocity of `5 m s^(-1)` is doubled, so the velocity becomes `5 xx 2 = 10 m s^(-1)`.
Now, Kinetic energy `= (1)/(2) mv^(2)`
`= (1)/(2) xx 2 xx (10)^(2)`
`= (1)/(2) xx 2 xx 100`
= 100 J
Thus, when the velocity of object is doubled, then its kinetic energy becomes 100 J.
(ii) In the second case, the velocity of `5 m s^(-1)` is increased three times so the velocity becomes `5 xx 3 = 15 m s^(-1)`.
Now, Kinetic energy `= (1)/(2)mv^(2)`
`= (1)/(2) xx 2 xx (15)^(2)`
`= (1)/(2) xx 2 xx 225`
= 225 J
Thus, when the velocity of object is increased three times, then its kinetic energy becomes 225 J.