Question

A particle A of mass $\frac{10}{7}kg$ is moving in the positive direction of $x-$axis. At initial position $x=0$, its velocity is $1m{s}^{-1}$, then its velocity at $x=10$ is in $m/s$ (use the graph given).

• A. $4m/s$
• B. $2m/s$
• C. $3\sqrt{2}m/s$
• D. $100/3m/s$

Answer 1

The correct option is A $4m/s$

Area under P-x graph =

$\int Px$

$\underset{1}{\overset{v}{\int }}mdvv\frac{dx}{dt}(\because \frac{dx}{dt}=v)$

$\underset{1}{\overset{v}{\int }}m{v}^{2}dv$

${{\left[\frac{m{v}^3}{3}\right]}_1}^v$

$\frac{m}{3}[v^3-1]...............\left(1\right)$

Area under $OABC=30$……………(2)

From equation (1) and (2)

$\frac{m}{3}[v^3-1]=30$

$\frac{10}{7\times 3}[v^3-1]=30$

$v^3=64$

$v=4m/s$