Question

Velocity-time graph of the particle is shown in figure. Find the displacement of the particle.

• A. $7\text{m}$
• B. $11\text{m}$
• C. $5\text{m}$
• D. $15\text{m}$

Answer 1

The correct option is B $11\text{m}$


From diagram,

$\tan \theta =\frac{4}{BC}=\frac{2}{CD}$

$\frac{CD}{BC}=\frac{1}{2}\Rightarrow \frac{CD}{BC}+1=\frac{1}{2}+1$

$\therefore BC=\frac{2}{3}BD=\frac{2}{3}\times 2=\frac{4}{3}$

As we know that net area of $v-t$ graph gives displacement.

$\therefore s=$ area of graph

$s=[\frac{1}{2}\times 4(2+\frac{13}{3})]-[\frac{1}{2}\times 2\times \frac{5}{3}]$

$\therefore s=\frac{38}{3}-\frac{5}{3}=11\text{m}$

Hence, option $\left(\text{B}\right)$ is correct.