## Newton’s low of motion

Newton gave three laws governing the motion of bodies.

1) First law- A body continues to be in its state of rest or of uniform motion along a straight line, unless it is acted upon by same external force to change the state.

2) Second low- The rate of change of linear momentum of a body is directly proportional to the external force applied on the body and this change takes place always in the direction of the applied force.

3) Third law-To every action, there is always an equal and opposite reaction. The action and reaction act on different bodies, hence they never cancel each other.

### The equation of motion

Let u = initial velocity of body, a = uniform acceleration of the body, v= velocity of the body after time t, s= distance travelled by body in time t, D_{n} = distance travelled by body in nth second.

1) **The equation of motion for accelerated body are**:

v= u + at

s=ut+1/2at^{2}

v^{2}= u^{2}+2as

D_{n} =u+a/2(2n-1)

2) **The equation of motion for retarded body here a is negative**:

v= u – at

s=ut-1/2at^{2}

v^{2}= u2+2as

D_{n} =u-a/2(2n-1)

3) **The equation of motion for a body falling down under gravity**:

Here a=+g

v= u + gt s=ut+1/2gt^{2}

v2= u2+2gs

D_{n} =u+g/2(2n-1)

4) **The equation of motion for a body going up under gravity**:

Here a=-g

v= u – gt

s= ut- 1/2gt^{2}

v^{2}= u^{2} – 2gs

D_{n} =u – g/2(2n-1)

5) Time taken to reach the maximum height is t = u/g

6) Total time taken by body in going up and coming down , T = 2t = 2u/g