Question

The diagram shows the velocity against time graph for the motion of a body along a straight path. What is its displacement in the first $5\text{s}?$

• A. $3\text{m}$
• B. $5\text{m}$
• C. $7\text{m}$
• D. $9\text{m}$

Answer 1

The correct option is D $9\text{m}$

We know that area under the velocity-time curve gives the displacement.

So,

Displacement $=$ Area of trapezium $\text{OABC}+$Area of triangle $\text{BCD}+$Area of triangle $\text{DFE}$

$\Rightarrow d=\frac{1}{2}\times (2+4)\times 3+\frac{1}{2}\times 1\times 4+\frac{1}{2}\times 1\times (-4)$

$\Rightarrow d=9\text{m}$

Hence, option $\left(D\right)$ is the correct answer.