A burst of compressed air pushes a pellet out of a blowpipe. The force exerted by the air on the pellet is given by \(F(t)=F_{0} e^{-t / \tau}\), where \(\tau\) is called a time constant because it has units of time.

(a) What does \(F_{0}\) represent?

(b) What is the momentum of the pellet after an interval equal to one time constant has elapsed?

(c) What is the momentum after an interval equal to five time constants has elapsed?

(d) What is the final momentum of the pellet after a long time interval has elapsed? \((e)\) If \(\tau=0.50 \mathrm{~ms}\), after how long a time interval has the momentum reached \(95 \%\) of its final value?