Question

please proof that s=ut+1/2at^2

Answer 1

Please follow the above diagram

Let us suppose that an object in uniform acceleration 'a' and it has covered the distance 's' within time 't'. From the graph, the distance covered by the object during time 't' is given by the area of quadrangle DOEB.

s = area of quadrangle DOEB
= area ( rectangle DOEA + triangle DAB)

s = (AE + OE) +( 1/2 * [AB + DA])

But AE = u, OE = t and (OE = DA = t)
AB = at...........(AB = CD)........{from (I)}

s = u*t + 1/2 * at * t
s = ut +1/2 at^2
HENCE PROVED

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