How to derive position time graphically
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From the Fig. the distance traveled s by the object is the area of the trapezium OABC.
Now
Area of OABC= area of the rectangle OADC + area of the Δ ABD
∴s= OA × OC + 12 (AD × BD) .......(4)
Substituting OA = u, OC = AD = tand BD = at, in (4) we get
s=u×t+1/2(t×at)
⇒s=ut+1/2at2 .......(5)
Now
Area of OABC= area of the rectangle OADC + area of the Δ ABD
∴s= OA × OC + 12 (AD × BD) .......(4)
Substituting OA = u, OC = AD = tand BD = at, in (4) we get
s=u×t+1/2(t×at)
⇒s=ut+1/2at2 .......(5)
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