- Books Name
- Science Made Easy Science Book

- Publication
- Science Made Easy

- Course
- CBSE Class 9

- Subject
- Science

**Statement of Second Law of Motion**

→ Rate of change of momentum of an object is proportional to applied unbalanced force in the direction of force.

Mathematical expression

Suppose, Mass of an object = m kg

Initial velocity of an object = u m/s

Final velocity of an object = v m/s

∴ Initial momentum, p_{1 }= mu

Final momentum, p_{2} = mv

∴ Change in momentum = Final momentum – Initial momentum

= mv – mu

= m(v – u)

**∴ Rate of change of momentu**m = Change in momentum/Time taken

= m(v-u)/t

• According to 2nd law, this rate of change is momentum is directly proportional to force.

We know that, a = (v-u)/t (From 1st equation of motion)

∴ F = kma

where, k is a constant. Its value can be assumed as 1.

∴ F = 1 × m × a = ma

**• SI unit = kg m/s ^{2} or Newton**

**1 Newton**: When an acceleration of 1 m/s^{2} is seen in a body of mass 1 kg, then the

force applied on the body is said to be 1 Newton.

**Proof of Newton’s First Law of Motion from Second Law**

→ First law states that if external force F = 0, then a moving body keeps moving with the same velocity, or a body at rest continues to be at rest.

∴ F = 0

We know, F = m(v-u)/t

(i) A body is moving with initial velocity u then,

m(v-u)/t = 0 ⇒ v – u = 0

∴ v = u

Thus, final velocity is also same.

(ii) A body is at rest i.e., u = 0

Therefore, from above u = v = 0

So, the body will continue to be at rest.