Question

Derive the following equations of motion
a) V = U + at
b) S = Ut + 1⁄2 at2
c) V2 = U2 + 2 aS

Answer 1

Answer:

a》Final velocity (v) = Initial velocity (u)+acceleration (a) ×Time (t)

=>a=v-u/t

=>at=v-u

=>at+u=v

=>v=u+at

b》Displacement (s) = ut+1/2at²

Distance=Average velocity×time

Average velocity = v+u/2

= u+at+u/2 (v = u+at)

= 2u+at/2

= 2u/2+at/2

= u+1/2at

s = (u+1/2at)×t

s = u+1/2at²

c》v²=u²+2as

s = v×t

Average velocity = v+u/t

v = u+at

=>t = v-u/a

s = v+u/2 × v-u/2

=> s = (v+u)(v-u)/2a

=> 2as = v²-u²

=> v²-u² =2as

=> v²= 2as + u²

=> v² = u²+2as