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?

Answer 1

Given:

Mass of the object = m

The velocity of the object v = 5 m s⁻¹

Kinetic energy E_K = 25 J

∴ E_K = `1/2 mv^2`

⇒ `25 = 1/2 m xx (5)^2`

⇒ `25 = 1/2 xx m xx 25`

⇒ `(25 xx 2)/25 =m`

⇒ m = 2 kg

Case I: When the velocity is doubled.

Mass of the object = m

i.e., v = 5m × 2 

= 10 m s⁻¹ 

∴ Kinetic energy (E_K) = `1/2"mv"^2`

= `1/2 xx (2) (10)`

= `1/2 xx 2 xx 100`

= 100 J

Case II: When the velocity is increased three times.

i.e., v = 3 × 5 = 15 m s⁻¹, m = 2 kg

Kinetic energy (E_K) = `1/2mv^2`

= `1/2 (2) (15)^2`

= 225 J