Force is the push or pull the body undergoes when it interacts with the other. It is expressed in Newtons (N).

The force F is defined as the rate of change of momentum given by,

F = $\frac{dp}{dt}$.

Where, dp is the momentum change, dt is the time change.

In terms of momentum, the force is given by,

F = $\frac{d (m \vec{v})}{dt}$.

Where, m is the mass and v is the velocity.

The rate of change of velocity with time is force given as,

F = m $\frac{dv}{dt}$.

Where, rate of change of velocity with time is acceleration.

Force is product of mass and acceleration.

Hence,

Force formula is given by,
F = ma.
Where, m is mass and a is acceleration.

Force Solved Examples

Below are given some examples on force:

Question 1: A girl buys a moving toy of mass 2.5 kg. If it moves with acceleration 5 m/s$^2$, calculate the force needed to move it.
Solution:
Given: Mass of toy m = 2.5 kg, acceleration a = 5 m/s$^2$.

The force is given by,
F = ma
F = 2.5 kg $\times$ 5 m/s$^2$
F = 12.5 N

Therefore, 12.5 N of force is needed to move toy.

Question 2: A body moves with the momentum of 2000 kg m/s in time 2 min. Calculate its force.
Solution:
Given: Momentum p = 2000 kg m/s, time t = 120 s

The force is given by,
F = $\frac{p}{t}$

F = $\frac{2000\ kg\ m/s}{120}$

F = 16.67 N.

Therefore, 16.67 N of force is needed to move the body.