Question

By how much willl the Kinetic energy of a body
increase of its speed is doubled?​

Answer 1

Answer:

If the speed of an object is doubled by increasing its velocity, its kinetic energy becomes four times its initial value. Thus kinetic energy increases by four times when its momentum is doubled. Hence kinetic energy of a body is increased most by doubling its speed.

Answer 2

To Find :

By how much will the kinetic energy of a body increase if its speed is doubled.

Solution :

■ Kinetic energy is a energy which a body possesses by virtue of being in motion.

• It is a scalar quantity having only magnitude.
• It can't be negative as speed is always positive$.$
• SI unit : J (joule)

Kinetic energy of a body of mass m moving at a speed of v is given by

• k = 1/2 mv²

In thus case, mass of body remains constant so we can say that kinetic energy of body is directly proportional to the square of its velocity.

• k ∝ v²

⇒ K'/K = v'²/v²

ATQ, velocity is doubled; v' = 2v

⇒ k'/k = (2v)²/v²

⇒ k'/k = 4

⇒ k' = 4k

∴ Kinetic energy of body will increase 4 times.