Prove that v² = u² + 2as.
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As we have already discussed earlier, motion is the state of change in position of an object over time. It is described in terms of displacement, distance, velocity, acceleration, time and speed. ... v = u + at. v² = u² + 2as.
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take Time as the variant and write it as t.
from 1st formula, you could find that t=v-u/a. use this variant in the 2nd formula.
S=u(v−u/a)+1/2a(v−u/a)^2
now take 1/2a to the LHS AND cut those a in denominator.multily 2 to RHS.
⇒2aS=2u(v−u)+(v−u)^2
now multiply u with v and -u in first case and simplify (v-u)^2
⇒2aS=2uv−2u^2−v^2−2uv−u^2
⇒2aS=v^2−u^2
take v^2 to LHS and 2as to RHS
⇒v^2=u^2+2aS
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