Question

Derive s=u + ut + 1/2 at by graphical method

Answer 1

Answer:

Explanation:

Acceleration is defined as rate of change of velocity.

 

hence acceleration a = (v-u)/t  ..................(1)

 

where u and v are initial and final velocity respectively and t is time taken to change velocity from u to v.

 

eqn.(1) can be rewritten as,  v = u+at ....................(2)

 

Let us asume te motion is with constant accelerated motion and its acceleration is a

 

Let in time t, the velocity is changed from u to v. Average velocity is (u+v)/2

 

distance S travelled in time t  = [ (u+v)/2 ] t .......................(3)

 

in Eqn.(3), let us substitute for v from eqn.(2), then distance S = [ (u+u+at)/2 ] t   = u t + (1/2) a t2