why rate of change of anything involves time
Answers
Well, suppose you are going to somewhere. Suppose your mom told you to market some products required for cooking purpose, and the actual market is very far away from your home. It is of course not a better way to walk from your home to the market. You should take a bicycle. Now, time is limited. So, you should ride bicycle at a speedy rat such that you take less time and the work can be successfully done.
Hence, we can conclude that whenever we are coming across the term "RATE", we are giving the actual importance to "TIME''. Thus, rate of change of anything involves time, because it is associated with time. It can be directly or indirectly related to it.
Now, let us take two popular examples of the fact of "RATE OF CHANGE" from physics.
[1] ACCELERATION : Rate of change of velocity is called acceleration. Let a body moving with an initial velocity of "u" m/s accelerates more, attaining a velocity of ''v" m/s at time "t".
Acceleration = (v-u)/t
[2] MOMENTUM : The product of mass of a body and velocity with which the body is moving is termed as linear momentum. Let the velocity of a body changes from "u" m/s to "v" m/s (v>u).
Then, change in momentum = (mv-mu) which can also be written as m(v-u).
Now, rate of change of momentum will be equal to (mv-mu)/t.
So, whenever we are saying "rate", it significantly represents the time. For example, if rate of speed increases, time taken to reach the destination decreases.