Speeding

How to get the resistance of fluids Newton's law F = ma?

Show that the velocity versus time of a particle falling from rest under the influence of gravity and a viscous force of the form f =- bv is given by v = ((mg) / b) (1-e ^ (- (bt) / m)) *.

Fg = mg = Fvis BV = FG-F =- bv A Fvis mg vterm terminal velocity, = * == vterm b> vterm mg = mg / b and b = g vterm * / m speed approaches maximum speed with an acceleration dv / dt = F / m = (mg-bv) / m = g-BV / m = b * vterm / m – BV / m = (vterm-v) * b / m. This is a problem of exponential decay, where vterm-v decays to 0 with a constant rate = b / m. (See ref.) Resolve, vterm vterm-v = ^ e * (*- tb / m) v ==> = vterm * (1-e ^ b * (-t / m)) = (mg / b) ^ * (1-e (-bt / m)).

P&W Northbound Speeding Past Uxbridge MA.