**Question**

**State Newton’s laws of motion. Establish the relation F = ma. **

**Answer**

**Newton’s laws of motion are:**

- An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
- The rate of change of momentum of an object is directly proportional to the applied force and takes place in the direction in which the force acts.
- For every action, there is an equal and opposite reaction.

Rate of change of momentum = Δp/t

= m(v-u)\over t [∵ Δp = m(v-u)]

= ma [∵ a = (v-u)\over t]

Now, according to Newton's second law of motion, the rate of change of momentum of an object is directly proportional to the applied force and takes place in the direction in which the force acts.

∴ F ∝ ma

or F = kma

where k is a constant. Here k = 1

Thus, F = ma

or, Force = mass × acceleration