Differentiation and Newton's second law

Derivative play a vital role in Physics. To understand the concept of derivative we need to know the problems of in detail. It was the Newton introduce the concept of differentiation while dealing with the laws of motion. He stated in his second law that force is directly proportional to the time rate of change of linear momentum

F=dp/dt

Where F is the force
p is the linear momentum and
t is the time

Now imagine the mass of a particle is constant then

F = m dv/dt
Therefore dv/dt represents the acceleration

Let v = const
Then change in velocity is zero therefore it is observed that no force is required to maintain its motion.

Similarly if velocity increases linearly with time

v = ct then v+dv = c( t+dt)

Or dv = c dt or dv/dt = c

Hence F = mc = constant