# Is kinetic energy on a body in vacuum = 0?

We know kinetic energy =$$\frac{1* mv^2}{2}$$- $$\frac{1* mu^2 }{2}.$$.

u=initial velocity & v=final velocity.
So , for a body in uniform translational motion I.e acc=0 & velocity is constant. Considering u = v from starting. Considering body in vacuum

Q: Will the kinetic energy of this body be 0 ?

Continued Question: If yes , then if this Body crushes onto another body. Will the transfer of kinetic energy also be 0?

No. The equation you wrote represents the change in kinetic energy due to a change in the speed of motion. Energy is required to start the motion, in a vacuum, the body stores the terminal energy with no loss (no resistance), thus it maintains a constant speed, $$v$$. When it runs into an immobile body, the velocity becomes the initial velocity at contact and transfers the energy through collision.

• What is the value we will write for kinetic energy here then ? Apr 21, 2022 at 4:44
• So , if a cycle starts from u = 0 at t=1 and end up with v=10m/s at t=2 and at t=3 v=100m/s after which velocity is 100m/s constant. So , should we say 0+10+100/3 = ‘V’ ? Apr 21, 2022 at 5:28
• The average velocity is the total distance traveled divided by the total travel time.
– r13
Apr 21, 2022 at 6:04
• Note, you stated that u = 0 from t = 0 to t = 1, so in the first second the car is idling (no motion), the time in idle should be subtracted from the total time of "travel (motion)", so the average velocity is 55.
– r13
Apr 21, 2022 at 15:30
• KE = mV^2/2. "v" is the "instantaneous" velocity with a constant value (v = constant). Please note the word "average", was a mistake. Sorry to cause the confusion.
– r13
Apr 21, 2022 at 20:08

The kinetic energy of a body is not an absolute, it is dependent on the body's velocity with respect to your particular reference frame. A person standing on the ground may watch a train speed past with a high velocity and a large amount of KE. But to a person on the train, the train has zero velocity and zero KE.

A body moving with constant velocity may or may not have zero KE, depending entirely on your reference frame and what you observe that constant velocity to be. If that constant velocity is zero (the object is not moving with respect to you), the object has zero KE. Another observer may see that same object moving with a non-zero velocity (it is moving relative to them), and to them the object has non-zero KE. There is always one reference frame in which an object with constant velocity has zero KE (the one in which it has zero velocity), and infinitely many reference frames in which it does not.

If a collision occurs, clearly both objects cannot be stationary with respect to a single observer (otherwise they would never collide). One or both of the objects must have KE (depending on reference frame), so the system has non-zero KE which will be redistributed upon collision. No matter what reference frame you choose, a system of colliding objects cannot have zero KE.