Prove that F = ma

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The force exerted on a system must be equal to the time rate at which its momentum is changing, according to Newton’s second law of motion. The formula of newton’s second law: f = m a. An illustration of Newton’s second law of motion:

Now we have To prove:

F = m a

According to newton’s second law force is given by,

F = dP/dt

But P = mv

Substituting the values

So F = d (mv)/dt

F = m.a [As a = dv/dt]

Table of content


Types of Force

An object’s state of motion or dimensions can change as a result of force, a physical cause. The push or pull on a mass-containing item changes its velocity. Based on their uses, forces can be divided into two categories:

  • Contact forces are defined as forces that affect a body directly or indirectly through a medium.
  • Non-contact forces are those that operate through voids without coming into physical touch with the body.

Applications of Newton’s Second Law

  • Kicking a ball

We use force in a precise direction when we kick a ball. The force we provide to the ball increases as we kick it harder, which causes the ball to move farther.

  • Pushing a cart

In a grocery store, an empty cart is simpler to maneuver than one that is filled, and heavier loads call for greater acceleration.

  • Two people walking

If there are two persons walking, and one of them is heavier than the other, the slower-moving person will walk because they are moving more quickly.

Therefore, proved.


Prove that F = ma

It is proved that F = ma. Newton’s second law of motion states that the force acting on a system must be equal to the rate at which its momentum is changing over time. The various applications of this law include two people walking, pushing a cart, and kicking a ball.

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