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all equations of motion?
Asked by kartikbhartiya613 | 28 May, 2021, 02:36: PM
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

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(2) Second equation is relation between displacement S , initial velocity u and accelertion a

"  S = ( u t ) + (1/2) a t2  "

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 t2

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(3) Third equation is relation between displacement S , inital velocity u , final velocity v and acceleration a .

" v2 = u2 + ( 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 ) = v2 - u2

v2 = u2 + ( 2 a S )
Answered by Thiyagarajan K | 28 May, 2021, 03:56: PM

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