The velocity - time graph for linear motion of an object is as shown. Find
(a) The distance travelled and
(b) Displacement for the interval between 5 s and 40 s.

Explanation

From velocity - time graph

`A_(1)=(1)/(2){20-5}xx(4-2)=(1)/(2)xx15xx2=15m`
`A_(2)=(20-5)xx2=15xx2=30m`
`A_(3)=(1)/(2)xx(25-20)xx2=(1)/(2)xx5xx2=5m`
`A_(4)=(1)/(2)xx(30-25)xx2=(1)/(2)xx5xx2=5m`
`A_(5)=(1)/(2){2+4}xx{40-30}=(1)/(2)xx6xx10=30m`
`"Total distance"=(A_(1)+A_(2)+A_(3)+A_(4)+A_(5)`
`=15m+30m+5m+5m+30m=85m`
`"Total displacement"=A_(1)+A_(2)+A_(3)+(-A_(4))+(-A_(5))`
`=15m+30m+5m+(-5m)+(-30m)`
`=15m`