Heres a problem I cant get I've managed to solve equations like this without involving the equation for friction, but this is slightly more taxing, for me...
a ball of mass
m, position x(t) and velocity v(t) = dx/dt, where t is time. The equation of
motion of the ball is
dv/dt = −μmg ,
where the only force on the ball is the friction,
μ > 0 is the constant coefficient of friction and g the acceleration
due to gravity.
Ball starts with initial speed V0, at position x = 0 and t = 0.
(a)Solve equation of motion and determine v(t).
(b)Solve dx/dt = v(t), using the result from part (a), and determine x(t).
Find time T at which ball stops.
If someone could get me started I'd appreciate it, what do I need to do to deal with the friction part?
I already know
dv/dt = -k/m*v => int dv/v = -k/mdt
v(t) = exp(-k/mt+C) = C'exp(-k/mt)
but this doesn't account for friction...