# ^Kinetic energy

**^Kinetic energy **

Kinetic means motion. A mass ‘m’ moving at

As both m & v^{2} are + ve & scalar, thus the KE of a body is always a +ve scalar quantity. Where as linear momentum is vector and always directed in the direction of velocity.

KE of a system of particles is the sum of kinetic energy of all of its constituent particles. i.e.

KE of a body depends upon the frame of reference. e.g. a person sitting in a moving bus has some KE w.r.t. the person standing at rest on road but no KE w.r.t. the persons in sitting in the same bus.

Actually KE is defined as the amount of work done to accelerate a body from rest.

Proof:

Rest means both linear momentum & KE zero. A body can’t have KE without linear momentum & vice – versa. Using the relation

we can say that

- If the linear momentum of a body is doubled, then its KE becomes 4 times.
- If the KE of a body is doubled, then its linear momentum becomes
- If a light body and a heavy body have same linear momentum, then lighter body will have greater KE.
- If a light body and a heavy body have same KE, then heavier body will have greater linear momentum.