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 
 
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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 | 28th May, 2021, 03:56: PM