# If momentum of an object is doubled, then what is the change in its kinetic energy?

##### 2 Answers

Percentage increase in kinetic energy is

#### Explanation:

Momentum of a body of given mass, is directly proportiional to its velocity. In fact momentum is mass multiplied by velocity.

Kinetic energy of a body of given mass, is directly proportiional to its square of its velocity.

When momentum is doubled, mass remaining constant, this means velcity is doubled.

Hence, kinetic energy becomes

and percentage increase in kinetic energy is

when the momentum is doubled, the kinetic energy goes up by a factor of 4 which represents a 300% increase.

#### Explanation:

Let's start by writing down some equations that we know for momentum and kinetic energy:

Kinetic energy is given by

while the momentum is

Both of these quantities is dependent on the mass ,

We know the relationship of momentum before and after:

then we can divide through by the mass to get rid of it in the relationship:

What we are looking for is the kinetic energy before and after:

let's factor out a

Therefore, when the momentum is doubled, the kinetic energy goes up by a factor of 4. This represents a 300% increase in K.E.

The starting K.E. is set to 100% and we end with 400% of the original K.E. representing a 300% increase.