Question

Use velocity time graph to derive the relation s=ut+1/2at^2

Answer 1

Distance travelled = Avg velocity * time

S=(u+v)/2*t

[But v=u+at]

S={u+(u+at)}/2*t  

S={(2u+at)/2}*t  

S=ut+1/2at^2

Answer 2

ANSWER:-

Let the distance travelled by the body be “s”.

We know that

Distance = Average velocity X Time

Also, Average velocity = (u+v)/2

.: Distance (t) = (u+v)/2 X t …….eq.(1)

Again we know that:

v = u + at

substituting this value of “v” in eq.(2), we get,

s = (u+u+at)/2 x t

=>s = (2u+at)/2 X t

=>s = (2ut+at^2)/2

=>s = 2ut/2 + at^2/2

or s = ut +1/2 at^2.

THIS IS CALLED THE 2nd EQUATION OF MOTION.

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