Question

How far does the runner whose velocity time graph is shown in figure travel in 16 s?

• A. 100 m
• B. 200 m
• C. 400 m
• D. 800 m

Answer 1

The correct option is C 400 m

The velocity of an object is given by
$v=\frac{dx}{dt}$
$\Rightarrow dx=vdt$
$\Rightarrow$ Displacement covered = Area under the $v-t$ curve
Dividing the graph into following triangles and rectangular segment.

Displacement =Area of $\Delta ABI+\text{Rectangle}IBCH+\Delta CJD+\text{Rectangle}JEFH$
$\Rightarrow \text{Displacement}=\frac{1}{2}\times 2\times 32+32\times 8+\frac{1}{2}\times 2\times 16+16\times 6$
$\Rightarrow \text{Displacement}=400m$