Question

A particle of mass 2 kg is moving under the influence of a force F(x) = (3/vx) N. If the velocity of the particle at x = 2 m is v = 6 m/s, what is its speed at x = 7 m

Answer 1

$a=\frac Fm=\frac 3{2\sqrt x}~\frac m{s^2},$

$v_1=\int a=3\sqrt x+C,$

$6=3\sqrt 2+C,$

$C=6-3\sqrt 2,$

$v_2=3\sqrt 7+6-3\sqrt 2\approx 2.3~\frac ms.$