Motion

EQUATIONS OF UNIFORMLY ACCELERATED MOTION

• Equations of motion are the equations which give relation between velocity, acceleration, distance covered, time taken for a body in uniform acceleration.
• The three equations of motions are:
  • First equation of motion :
    $v = u + at$
  • Second equation of motion:
    $s = ut + \frac{1}{2}a{t}^2$
  • Third equation of motion :
    $v^2 – u^2 = 2as$

FIRST EQUATION OF MOTION

The first equation of motion is:

Where,  u: Initial velocity

v: Final velocity

t: Time

a: Acceleration

Derivation:

We know that acceleration is the rate of change of velocity with time.

Hence, acceleration is represented as:

Taking Final velocity as v and the initial velocity as u,

We get:

By rearranging the equation, we get:

SECOND EQUATION OF MOTION

The second equation of motion:

Where,

s: distance

u: Initial velocity

v: Final velocity

t: Time

a: Acceleration

We get:

From the first equation of motion we have, . Putting this value v in equation (1),

THIRD EQUATION OF MOTION

The third equation of motion:

Where,

s: distance

u: Initial velocity

v: Final velocity

t: Time

a: Acceleration

Let a body start with initial velocity u and after covering distance s under uniform acceleration a, its velocity becomes v in t seconds.

 From the second equation of motion, we have,

Here lets substitute the value ofwith respect to thefrom the first equation of motion:

We get,