Question

A particle starts from the origin at time $t=0$ and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $t=5\text{s}$ ?

• A. $10\text{m}$
• B. $6\text{m}$
• C. $3\text{m}$
• D. $9\text{m}$

Answer 1

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

Distance travelled by the particle is of the particle in $v-t$ graph is area under the graph

Hence,
$S=$ area under graph (time $t=0\text{to}5\text{s}$)
$S=$ area under graph (time $t=0\text{to}2\text{s}$) + area under graph (time $t=2\text{to}4\text{s}$) + area under graph (time $t=4\text{to}5\text{s}$)

$S=\frac{1}{2}\times 2\times 2+2\times 2+3\times 1=9\text{m}$.