From the following v-t graph, find the displacement for time interval `t=3` to `t=12 s`.

Explanation

To determine the displacement for `t=3` to `t=12 s`, we require velocities at these instances.

`tan alpha=v_(1)/3=20/5impliesv_(1)=12 m//s`

`tan beta=v_(2)/((15-12))=20/((15-5))impliesv_(2)=6 m//s`

Area of trapezium (1)`=1/2(12+20)xx2=32`
Area of trapezium (2) `=1/2(6+20)xx7=91`
For `t=3` to `12 s`, Displacement `=32+91=123 m`