$!$

Required information

Problem $11\mathrm{.}024-$ Particle motion: velocity$-$dependent acceleration

The acceleration of a particle is defined by the relation $a=-k\sqrt[\phantom{2}]{v},$ where k is a constant. Know that $x=0$ and $v=81\frac{m}{s}$ at $t=0$ and that $v=38\frac{m}{s}$ when $x=22m.$

Problem $11\mathrm{.}024.$a $-$ Obtaining position from velocity$-$dependent acceleration by integration

Determine the velocity of the particle when $x=20m$

The velocity of the particle is $\frac{m}{s}.$