## Newton's Second Law

The first law of motion indicates that when a balanced external force acts on an object, its velocity changes and the object gets accelerated. In this article, we would discuss how the acceleration of an object depends on the force applied to it and how we measure a force. Newton's second law is the quantitative value.

## What is Newton's Second Law of Motion?

Newton's second law of motion states that the acceleration of the body depends upon two variables, that is, the net force applied and the mass of the object. The acceleration of the object is directly proportional to the net force acting on the body and inversely proportional to the mass of the object. So it can be written as-

**a = F/ m** (This equation shows that acceleration is inversely proportional to the mass of the body)

**F = ma**( This equation shows that acceleration is directly proportional to the net force acting on the body)

## Mathematical Formula of Second Law of Motion

Suppose a body of mass(m) is moving in a straight line with its initial velocity(u). It is uniformly accelerated to velocity(v) in time(t) by the application of a constant force(F) throughout the time(t).

The initial and final momentum of the body becomes,

p1 = mu

p2 = mv

Therefore, Change in Momentum ∝ p2 – p1

∝ mv – mu

∝ m × (v – u)

Velocity is equal to displacement upon the time taken

Then, the rate of change of momentum ∝ m×( v − u )/t

The applied force will be, F ∝ m×(v- u)/t

F = k m(v-u)/t

**F = k ma **

Here, a = (v-u)/t is the acceleration.

F = Net force applied

m = mass of the body

k = proportionality constant

Formulation of Force for Changing and Constant Mass | |

For changing mass | F = m1v1-m0v0/t1-t0 |

For constant mass | F = m(v1 - v0/t1-t0) |

### SI Unit of Force

The SI units of mass and acceleration are kg and m/s² respectively.

1 unit of force = k × (1 kg) × (1 m/s²).

F = ma

**The SI unit of force is kg m/s² or newton, which has the symbol N.**

## Application of Second Law of Motion

Some of the applications of the Second law of motion are-

- Pushing of Car and Truck.
- Pushing of Shopping cart.
- Kicking a ball.
- Two people walking.
- Rocket Launch.
- Car Crash.

## Exercise based on Newton's Second Law

**Q1. A truck is moving with a velocity of 30m/s and it takes 5s to stop after the brakes are applied. Calculate the force exerted by the brakes on the truck if its mass along with the passengers is 1500 kg.**

**Solution: **According to the question,

The initial velocity of the motorcar, u = 30m/s

The final velocity of the motorcar, v = 0 m s-1

On substituting the values, we get F = 1500 kg × (0 – 30) m s-1/5 s

= – 9000 kg m/s² or – 9000 N.

The negative sign tells us that the force exerted by the brakes is opposite to the direction of motion of the motorcar.

**Q2.If there is a block of mass 4kg, and a force of 30 N is acting on it in the positive x-direction, and a force of 50 N in the negative x-direction, then what would be its acceleration?**

**Solution: **Net Force = 30N - 50N

Net Force = -20N

Acceleration = -20/4 = -5m/s²

The negative acceleration indicates that the block is slowing and its acceleration vector is moving in an opposite direction directed opposite to the direction of motion.