The equation of motion


The low of motion

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.

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, Dn = 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
Dn =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
Dn =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
Dn =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
Dn =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