Question

using velocity -time graph of uniformly accelerated motion along a straight line, derive the equation v^2-u^2=2as where symbols have their usual meaning.​

Answer 1

s=ut+1/2×a(t)^2. ...........(i)

v=u+at

this can be rearranged and written as

at=(v-u)/a

t=( v-u)/a. ...............(ii)

putting this value of t in equation (i)

s= [ u(v-u)]/a +1/2×a[(v-u)/a]^2

s= (uv -u^2)/a + [a(v^2+u^2-2uv)]/2a^2

s=(uv-u^2 )/a+( v^2+ u^2-2uv)/2a

s=(2uv-2u^2+v^2+u^2-2uv)/2a

2as= v^2-u^2