Problem

A particle having a velocity

v = v_0

t = 0

is decelerated at the rate

|\alpha| = \alpha\sqrt{v}

, where

\alpha

is a positive constant. a. The particle comes to rest at

t = \frac{2\sqrt{v_0}}{\alpha}

b. The particle will come to rest at infinity c. The distance travelled by the particle before coming to rest is

\frac{2v_0^{3/2}}{\alpha}

d. The distance travelled by the particle before coming to rest is

\frac{2v_0^{3/2}}{3\alpha}