Acceleration formula in terms of velocity and distance
Answers
- acceleration = distance up on velocity/ time taken ...
as we know .
v = u + at
v- u / a = t .............1.
put value of eq.1. in formula
s = ut + 1/2 at^2
s = u ( v - u / a ) + 1/2 a ( v - u / a ^2 )
s = 1/2 a ( v - u / a ) ^ 2 + u ( v - u / a )
in the underlined ___ identity (a-b)^2 = ( a^2 + b^2 -2 ab ) will be used.
s = 1/2 a ( v ^2 + u ^2 - 2vu /a^2) + u (v - u /a)
taking l.c.m of underlined —-__
s = 1/2 a ( v^2 + u ^2 - 2vu / a ^2 ) + ( uv - u ^2 / a )
the underlined a will be cut off as these are in mmultiplication with each other
s = 1/2 ( v^2 + u^2 - 2vu / a) + uv - u ^2 / a )
multiplying 1/2 with underlined______we get
s = ( v^2 + u ^2 - 2 vu / 2a ) + ( uv - u ^2 /a )
now taking l.c.m of the equation ...we get
s = ( v^2 + u^2- 2vu + 2vu - 2 u ^2. / 2a )
s = ( v^2 + u^2 + 0 vu - 2 u ^2. / 2a)
s = ( v^2 + u^2 - 2u^2 / 2a)
subtracting : u^2 - 2u ^2 = - u^2
s = ( v^2 - u^2 / 2a)
2as = v^2 - u^2
v^2 - u^2 = 2 as
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