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The velocity versus time graph of a body...

The velocity versus time graph of a body moving along a straight path is shown below.

(i) Calculate the distance covered by the body from t=0 to t=8s.
(ii) find its net displacement from t=0 to 8 s.

Text Solution

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(i) Distance covered by the body from t=0 to 8 s.
=Area under the v-t graph
`=(1)/(2)xx1xx20+1xx20+(1)/(2)xx1xx20+(1)/(2)xx1xx30`
`+2xx10+(1)/(2)xx2xx30+2xx10`
`=10+20+10+15+20+30+20=95`m
(ii) Displacement is positive from 0 to 3 s, negative for 3 to 4 s and positive from 4 to 8s.
`therefore` Total displacement in 0 to 8 s is
`=(1)/(2)xx1xx20+1xx20+(1)/(2)xx1xx20-(1)/(2)xx1xx30+2xx20+(1)/(2)xx2xx30+2xx10`
`=10+20+10-15+20+30+20=95` m
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