Question

A particle of mass $1kg$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$, then its velocity at $x=15m$ is

• A. $0$
• B. $20\sqrt{3}m{s}^{-1}$
• C. $20\sqrt{2}m{s}^{-1}$
• D. $20m{s}^{-1}$

Answer 1

The correct option is D $20m{s}^{-1}$

$K.E$ at $x=15m$=work done by force from $x=0$ to $x=15$

=Area enclosed

$\frac{1}{2}m{v}^2=\frac{1}{2}\times 5\times 20+\frac{1}{2}\times 20\times 5+20\times 5$

$=50+50+100=200$

$\frac{1}{2}\times 1\times v^2=200$

$v=20m/s$