Question

Derive the expression for position time relation by graphical method.

Answer 1

Heya,

Answer to your question is:-

Equation for distance –time relation

Distance covered by the object in the given time ‘t’ is given by the area of the trapezium ABDOE

Let in the given time, t the distance covered by the moving object = s

The area of trapezium, ABDOE

= Distance (s) = Area of △ABD+△ABD+Area of ADOE

⇒s=1/2×AB×AD+(OD×OE)
⇒s=1/2×AB×AD+(OD×OE)
⇒s=1/2×DC×AD+(u+t)
⇒s=1/2×DC×AD+(u+t)

[Since,AB=DC]

⇒s=1/2×at×t+ut
⇒s=1/2×at×t+ut
⇒s=1/2×at×t+ut
⇒s=1/2×at×t+ut

[∵ DC=at]

⇒s=1/2at2+ut
⇒s=1/2at2+ut

【⇒s=ut+1/2at²】

HOPE THIS HELPS YOU:-))
@Ashu