Question

Derive the equation of motion, 2as = v-u by graphical method.

Answer 1

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+

Area of ADOE

⇒s=12×AB×AD+(OD×OE)

⇒s=12×DC×AD+(u+t)

[Since, AB=DC

]

⇒s=12×at×t+ut

⇒s=12×at×t+ut

[∵ DC=at

]

⇒s=12at2+ut

⇒s=ut+12at2