Question

A body accelerates uniformly from its initial velocity u, to the final velocity, v, in time t. the distance travelled during this is s. If acceleration is donated by letter a, show that;

1. v = u + at 
2. s = ut + ½ at² . 
3. v² = u² + 2as.

Answer 1

1. v = u + at
   t×a=v-u×t
            t
   at = v−u
   v = u + at ……… (i)
2. s = ut + ½ at² .
   S=(u+v) t
        ( 2  )
   but from eqn (i)
   v = u + at
   S =(^2u/₂+½ at) t
   S =(u+½ at) t
   S = ut + ½ at² ----- (ii)
3. v² = u² + 2as. 
   S=(u+v) t  but t from eqn (i) = (v-u)
        ( 2  )                                     a
                            2a×s (u+v)(v-u) ×2a
                                        2      a
                             2as=(u+v)(v-u)
   2as = uv – u² + u² + v² – uv
   2as = v² – u²
   V² = u² + 2as ……. (iii)