# Force Equals Mass Times Acceleration

There are three laws of motion given by the famous scientist Sir Isaac Newton. To explain these laws first we explain the terms inertia, momentum and force. The inherent property of all bodies, by virtue of which they cannot change their state of rest or of uniform motion along a straight line on their own, is called inertia. Inertia depends on the mass of the body. More is mass of the body more is the inertia. There are three types of inertia one is inertia of rest second is inertia of motion and the third is inertia of direction. Momentum of a body is the measurement of the motion of the body. Thr force equal to the mass times acceleration explained by the Newton's second law of motion. In behaviour Newton third law of motion which gives force equals mass times acceleration is the real law of motion.

## Second law of motion which gives force equals mass times acceleration

According to second law of motion, the rate of change of linear momentum is directly proportional to the external force applied on the body and this change takes place always in the direction of the force applied. It means that if larger force is applied then momentum of the body changes by the faster rate and vice-versa.

The linear momentum of the body, p = m v

Rate of change of linear momentum = dp/ dt

According to the Newtonâ€™s second law of motion,

F is proportional to dp / dt

F = k dp / dt

Where k is the constant of proportionality.

F = k m d p / dt

F = k m a                   (d p /dt = acceleration)

Where  a is the acceleration produced in the body.

Experimentally we found that the value of k is 1, so

F = m a

This realtion prove that the force equls to mass times acceleration.

Force is a vector quantity and teh SI unit of force is Newton and the small unit of force is dyne.

1 Netwon = 100000 dyne

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## Examples based on force equals mass times acceleration

Example 1: A body of mass 3 kg moves with an acceleration of 5 metre per squared second by applying a force. Find the amount of force applied on the body.

Solution:

Mass = 3 kg, acceleration = 5 metre per squared second

According to the second law of motion

Force = mass times acceleration

F = 3 x 5 = 15 newton.

Example 2: A body of mass 25 kg is pulled by a force of 50 Newton. Find the acceleration produced in the body.

Solution: mass = 25 kg, Force = 50 Newton

According to the second law of motion

F = mass times  acceleration

Acceleration = F/ m = 50 / 25 = 2 metre per squared second

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