Question

The velocity-time graph of a body is shown in Fig.The displacement of the body in 8 s is

• A. 9 m
• B. 12 m
• C. 10 m
• D. 28 m

Answer 1

The correct option is C 10 m

Displacement by a $v-t$ graph is found by area under the curve.

Dividing graph into rectangle from $t\to 0to2$

trapezium from $t\to 2+3$, triangle from $t\to 3to4$

and $t\to 4to5$, rectangles from $t\to 5to6$

and $t\to 6to8$ where any any part in negative $y-axis$ is taken as negative

$\therefore$ Displacement $=(2\times 2{)}_{t\to to2}+(\frac{2+6}{2}\times 1{)}_{t\to 2to3}+(\frac{1}{2}\times 1\times 6{)}_{t\to 3to4}-(\frac{1}{2}\times 1\times 6{)}_{t\to 4to5}-(1\times 6{)}_{t\to 5to6}+(2\times 4{)}_{t\to 6to8}$

$=4+4+3-3-6+8=10m$