Kinematic Equations

Kinematic Equations represent the motions of a body moving with constant velocity or uniform acceleration.

When the body is moving with constant velocity or velocity increases with constant rate, then the body is moving with uniform positive acceleration. At this point, its initial velocity is zero and hence its acceleration is also zero. There is no change in velocity, so body is moving with uniform acceleration.

These Kinematic Equations are:

V_f = v_i + at     (i)

S = V_i  t + ½ at²   (ii)

V²_f = V²_i + 2aS   (iii)

By utilizing these equations, we can find the values of V_f, S, t, a and V_i.

Example, suppose a car is moving with a velocity of 300 km hr^-1 after a distance of .45 km at constant acceleration. Find the acceleration.

Here Vi = 0 , Vf = 300 km hr^-1 = 300 x 1000/ 1/3600 =  300 / 3.6 = 83.33 ms^-1

S = 0.45km = .45 x 1000 = 450m

a = ?

We Know V²_f = V²_i + 2aS

By putting Values and arrange the equation for a, we get:

a = V²f / 2 x S

a =  (83.33)² / 2 x 450

a = 83.33 x 83.33 / 900

a = 6943.8889 / 900

a = 7.715 ms^-2

So, it is all about Kinematic Equations for free fall body equations or motion equations for a body that is moving with uniform acceleration and its velocity is not changing along the path.