Kinematic Equations for uniformly accelerated motion along straight line

(i) Velocity time equation –

(ii) Displacement time equation –

(iii)Velocity displacement equation –

(iv)Displacement in nth second –

Consider a body of mass m having initial velocity u and after time t its final velocity becomes due to uniform acceleration.

We know that

Let the distance travel by a body be “S”

Substituting from (i) equation

(ii) We know

Again

Let be the displacement of the body in second

Let be the displacement in second

we know that

Displacement during nth second

**Derivation of equation for uniformly accelerated motion by calculus method.**

Consider an object having mass m initial velocity u at time t = 0 and final velocity at time due to uniform acceleration a.

If dv is small change in velocity in small time Interval dt

Integrate and take limit both side

Let ds be small displacement in small Interval dt

But

Taking** **limit both side

**Velocity displacement equation**

We know

Integrating both side with limit

**Displacement in n ^{th} second**

If then

and if , then

Integrating both side