# Equation of motion, velocity, position.

A particle of mass $m$ falls from rest at $t=0$ from a height $h$ above ground level, assumed to be at $z=0$, subject to its weight and a linear drag force (air resistance) $F = -mfv$ proportional to its velocity, where $f > 0$.

Write down the equation of motion. Find the velocity and position as functions of time.

Write down the equation that determines the time $t_1$ at which the particle reaches ground level.

Any help? Thanks.

• Draw a picture. Analyze the forces acting on the particle-mass. – amarney Mar 22 '17 at 19:45

Newton's 2nd law reads $$F_{net} = mx''(t) = mg - mfx'(t)$$ If you can solve an equation of the form $$x'' + ax' = b,$$ then you have your position with respect to time. Differentiate this to get your velocity function. Also, once one knows $x(t),$ you can get $t_1$ by setting $x(t_1) = 0$ and solving for $t_1.$