Example:

1. Interpret the expression ΔV /V and write it in terms of a differential. ΔV /V express the fractional change of velocity. It is the change within velocity divided by the velocity.   It can be written as a differential while ΔV is taken as an incremental change.

ΔV/V may be written as dV/V

2. Give the physical interpretation of the subsequent equation relating the  work  W   done  while  a  force  F  moves  a  body  by  a distance x .

dW  = Fdx

This equation involves the differentials dW and dx that can be interpreted in terms of incremental changes. The incremental amount of work completed equals the force applied multiplied by the incremental distance moved.

3. Give the physical interpretation of the subsequent equation relating the force, F will be applied to an object, its mass m, and its instantaneous velocity v and time t.

F= m(dv/dt)

This equation involves the derivative dv/dt; the derivative of the velocity with respect to time.  It is the rate of change of velocity along with respect to time. The force which is applied to an object equals the mass of the object multiplied by the rate of change of velocity with respect to time.

4. Provide the physical interpretation of the subsequent equation relating the acceleration a, the velocity v & the time t.

a= dv/dt

This equation involves the derivative dv/dt; the derivative of the velocity with respect to time. It is a rate of change. Here the acceleration equals the rate of change of velocity with respect to time.