Equation of motion

Describe the Newton's equation of motion?

Newton gave three laws governing the motion of bodies and equation of motion.
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.

equation of motion

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+1/2at²
v²= u²+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-1/2at²
v²= 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+1/2gt²
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- 1/2gt²
v²= u² - 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