Question

Show that the expression S=vit+½at² is dimensionally correct

Answer 1

Average velocity =initial velocity +final velocity / 2

that is, average velocity = u + v /2

also , distance travelled =average velocity ×time

so, s=(u+v) /2 ×t ........... (1)

from the first equation of motion we have, v=u+at. Putting this value of v in equation (1), we have :

s=[(u+u +at) ×t ]/2

s=[(2u + at) ×t ] /2

s=(2ut +at^) /2

s= ut +1/2 at^.