Question

The kinetic energy of an object of mass 2 kg moving with a velocity of 5 m/s is 25 J. What will be its kinetic energy only when its velocity is doubled? What will be its kinetic energy only when its mass is increased by three times?​

Answer 1

Given :

• Mass (m)= 2 kg
• Velocity(v) = 5 m/s
• Kinetic energy (KE)= 25 J

To find :

• KE when velocity is doubled
• KE when mass is increased by three times

Solution:

Kinetic energy is the energy possessed by the body due to its motion.

$\dag\boxed{\sf{KE =\dfrac{1}{2}mv^2 }}$

Case I: velocity is doubled

⇒ KE '= ½ x m x (2v)²

⇒ KE ' = ½ x m x 4v²

⇒ KE ' = 2mv²

Now let's substitute the values,

⇒ KE' = 2 x 2 x 25

⇒ KE ' = 100 J

Case II: Mass is increased by three times

⇒ KE" = ½ x 3m x v²

Now let's substitute the values,

⇒ KE" =  ½ x 3 x 2 x 25

⇒ KE" = 25 x 3

⇒ KE" = 75J

 

Answer 2

Answer :

$\sf● \: Known \: terms:-$

$\sf \blue{M} = \red{Mass \: of \: the \: object}$

$\sf \blue{V} = \red{Velocity \: of \: the \: object}$

$\sf \blue{K.E} = \red{Kinetic \: energy \: attain \: by \: object}$

$\sf \blue{J} = \red{Joule}$

Given :

➙ Kinetic energy attain by object, K.E = 25 J

➙ Velocity of the object, V = 5m/s

To find :

● Kinetic energy when velocity is increased three times.

Solution :

★ We know that, K.E

$\sf \red{=} ½ \: mv²$

$\sf \red{=} 25 = ½ \: m \: 5²$

$\sf \red{=} m = 2 \: kg$

$\: \: \: \: \: \: \: \: \: \: \: \: \: {{\underline{\pmb{\sf{\purple{\underline{( \: 1st \: Case \: )}}}}}}}$

■ If velocity is doubled.

Then,

$\sf \: Velocity \: of \: the \: object = 10 \: m/s$

$\sf \: Mass \: OS \: the \: object = 2 \: kg$

$\implies \sf \: K.E = \frac{1}{2} \: mv²$

$\implies \sf \: K.E = \frac{1}{2} \: 2 × 10²$

$\fbox \pink{ \sf \: K.E = 100 Joule}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: {{\underline{\pmb{\sf{\purple{\underline{( \: 2nd \: Case \: )}}}}}}}$

★ If velocity is three times.

Then,

$\sf \: Velocity \: of \: the \: object = 15 \: m/s$

$\sf \: Mass \: OS \: the \: object = 2 \: kg$

$\implies \sf \: K.E = \frac{1}{2} \: mv²$

$\implies \sf \: K.E = \frac{1}{2} \: 2 × 15²$

$\fbox \pink{ \sf \: K.E = 225 Joule}$

Hence, Kinetic energy when its Velocity is increased three times 225 Joule.