Question

By what factors does the kinetic energy of a body increase when its speed is doubled?

Answer 1

Answer:

The kinetic energy increases by a factor of 4.

Explanation:

Here we have been given to find by what factors the respective kinetic energy of the given body increases whenever its speed is doubled. For this we first see the formula of the kinetic energy which is as below:

Kinetic energy (K.E.) = $\frac{1}{2} mv^{2}$

Here m is the respective mass of the body and v is the velocity of the object.

Now here it has been mentioned that the velocity has been doubled. So we take the increased velocity to be $v_{2}$ and we take the initial velocity to be $v_{1}$

Now since the mass will remain the same in both cases there the kinetic energy becomes proportional to the square of the velocity of the body as below:

K.E ∝ $v^{2}$

Therefore let $K.E_{1}$ = Initial kinetic energy

$K.E_{2}$ = final kinetic energy with double velocity.

So here we have,

$\frac{K.E_{1}}{K.E_{2}} = (\frac{v_{1}}{v_{2}})^{2}$

and it is given that $v_{2} = 2 v_{1}$

∴ $\frac{K.E_{1}}{K.E_{2}} = (\frac{v_{1}}{2 v_{1}})^{2}$

⇒ $\frac{K.E_{1}}{K.E_{2}} = \frac{1}{4}}$

⇒ $K.E_{2}= 4 K.E_{1}$

Hence the kinetic energy increases by a factor of 4 whenever the velocity is doubled.

Answer 2

The kinetic energy is directly proportional to the square of the speed, so doubling the speed increases the kinetic energy by a factor of 4.

Explanation:

• The Kinetic energy is formed from rotational motion or translational motion.

• The S.I units of joules (J).

• The kinetic energy = 1/2mv².

• Translational kinetic energy is directly proportional to the square of the magnitude of velocity and the mass of the body.