Kinematic Equation

Description:

For uniformly accelerated motion, we can derive some relation between displacement, velocity, time and acceleration known as kinematic equations.

1. According to the definition of acceleration −

a = v - u/t

∴ v = u + at .....(i)

Where,

v = Final Velocity,

u = Initial Velocity,

a = Acceleration &

t = Time.

2. Average velocity is given by −

v_o = v + u/2

Displacement is given by −

S = v_ot

∴ S = (v + u/2)t

By substituting the value of v from first equation, we get −

S = (v + at + u/2)t

S = (2u/2 + at/2)t

∴ S = ut + 1/2at² ....(ii)

3. From first kinematic equation, we have −

a = v - u/t

Rearranging the equation, we get −

t = v - u/a

Displacement is given by −

S = v_ot

S = (v + u/2) (v - u/a)

S = v² - u²/2a

∴ v² = u² + 2as ....(iii)