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The figure denotes velocity-time graph, ...

The figure denotes velocity-time graph, displace ment is equal to

A

`y (x_(1)+x_(2)+x_(3))`

B

`y(x_(3)-x_(1))`

C

`y (x_(3)-x_(2)-x_(1))`

D

`(y)/(2) (x_(3)+x_(2)-x_(1))`

Text Solution

Verified by Experts

The correct Answer is:
D
The area enclosed between velocity-time curve and the time axis gives displacement.
OABC is trapezium. Side `OC = X_(3)`, side
`AB =(x_(2)-x_(1))`
Height = y
`therefore ` Area `=(1)/(2)xx" Height "xx` (Sum of parallel side)
Area `=(1)/(2)xxyxx(x_(3)+x_(2)-x_(1))`
`therefore" Displacement "=(y)/(2) (x_(3)+ x_(2)-x_(1))`
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