Question

A body of mass 0.5 kg travels in a straight line with a velosity $v$ = $5x^{3/2}$ . The work done by the net force during its displacement from x = 0 to x = 2 m is ?

• A. 50 J
• B. 45 J
• C. 25 J
• D. None of these

Answer 1

Answer: (A)

50 J

Mass of the body, $m=0.5kg$

Velocity of the body is governed by the equation, $v=a{x}^{3/2}$

Acceleration, $a=5m^{-1/2}{s}^{-1}$

Initial veleocty, $u$ (at $x=0$) $=0$

Final velocity, $v$ (at $x=2m$) $=20\sqrt{2}m/s$

Work done, $W=$ Change in Kinetic energy

$=\frac{1}{2}m(v^2-u^2)$

$=\frac{1}{2}\times \left(\right(10\sqrt{2}{)}^2-0^2)$

$=\frac{1}{2}\times 0.5\times 10\times 10\times 2=50J$