all equations of motion?

### Asked by kartikbhartiya613 | 28th May, 2021, 02:36: PM

Expert Answer:

### There are three equations of motion with uniform acceleration
(1) First equation is relation between velocities and acceleration
" v = u + a t " .............................(1)
where v is final velocity , u is initial velocity , a is acceleration and t is time taken to change velocity from u to v .
Equation (1) is derived from the definition of acceleration.
Acceleration is defined as rate of change of velocity.
If velocity changes from u to v in t seconds , then acceleration a = ( v - u ) / t ......................(2)
Frim eqn.(2) , we get , v = u + a t
----------------------------------------------------------------------
(2) Second equation is relation between displacement S , initial velocity u and accelertion a
" S = ( u t ) + (1/2) a t^{2} "
where t is time taken to get displacement S
Displacement S = average velocity × time
S = (1/2) ( u + v ) × t .............................................(2)
If we substitute for v using eqn.(1) , we get
S = ( u t ) + (1/2) a t^{2}
--------------------------------------------------------------------
(3) Third equation is relation between displacement S , inital velocity u , final velocity v and acceleration a .
" v^{2} = u^{2} + ( 2 a S ) "
Displacement S = average velocity × time
S = (1/2) ( v + u ) × t .............................................(3)
In above eqn.(3) , we eliminate time t using eqn.(1) by using the substitution t = ( v - u ) / a
We get , S = (1/2) ( v + u ) [ ( v - u ) / a ]
( 2 a S ) = v^{2} - u^{2}
v^{2} = u^{2} + ( 2 a S )

^{2}"

^{2}

^{2}= u

^{2}+ ( 2 a S ) "

Displacement S = average velocity × time

S = (1/2) ( v + u ) × t .............................................(3)

In above eqn.(3) , we eliminate time t using eqn.(1) by using the substitution t = ( v - u ) / a

We get , S = (1/2) ( v + u ) [ ( v - u ) / a ]

( 2 a S ) = v

^{2}- u^{2}v

^{2}= u^{2}+ ( 2 a S )### Answered by Thiyagarajan K | 28th May, 2021, 03:56: PM

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