Question

The kinetic energy of an object of mass, m moving with a velocity of 5 m s–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?

NCERT Class IX
Sciences - Main Course Book

Chapter 11. Work and Energy

Answer 1

K. E.  =  1/2 m v^2  =  1/2 * m 5^2  = 25 Joules
         =>  m = 2 kg

When the velocity becomes double:  ie.,  10 m/s

K. E.   =   4 times previous value = 4 * 25 J = 100 J
                 or, 1/2 m v^2= 1/2 * 2 kg * 10^2  Joules      =  100 Joules

  v  =  3 times = 15 m/s
KE will become  9 times original value ,as  KE is proportional to the square of the velocity
 
   K. E. =  1/2 m v^2 = 1/2 * 2 kg * 15^2  =  225 Joules

Answer 2

100J

225J

Solution :-

Given :

Kinetic energy of the object = 25 J

Velocity of the object, v = 5 m/s

To Find :

Kinetic energy when its velocity is doubled = ?

Kinetic energy when its velocity is tripled = ?

Solution :

First, we will calculate the mass 'm ' of the object.

We know,

$\boxed{\sf{}K.E = \dfrac{1}{2}mv^2}$

So,

$\sf{}:\implies 25=\dfrac{1}{2}\times m\times 5$

$\sf{}:\implies 25=\dfrac{1}{2}\times m\times 25$

1

$\sf{}:\implies 25\div \dfrac{1}{2}=m\times 25$

$\sf{}:\implies \dfrac{25\times 2}{25}=m$

$\sf:\implies \dfrac{50}{25}=m$

$\sf{}:\implies \dfrac{10}{5}$

$\sf\therefore m=2kg$

Now, if the velocity is doubled,

= 2 × 5

∴ 10 m/s

Kinetic energy when its velocity is doubled,

$\sf{}:\implies \dfrac{1}{2}mv ^{2}$

$\sf{}:\implies \dfrac{1}{2}\times 2\times 10^2$

$\sf{}:\implies \dfrac{1}{1}\times 1\times100$

$\sf{}:\implies \dfrac{1}{1}\times 1\times 100$

:

$\sf{}\therefore 100J$

Therefore,if the velocity is doubled its kinetic energy is equal to 100J

Now, if the velocity is doubled,

= 3 × 5

∴ 15 m/s

Kinetic energy when its velocity is tripled,

$\sf{}:\implies \dfrac{1}{2}mv^2$

$\sf{}:\implies \dfrac{1}{2}\times 2\times 15$

$\sf{}:\implies \dfrac{1}{1}\times 1\times 225$

$\sf{}\therefore 225J$

Therefore,if the velocity is tripled its kinetic energy is equal to 225J