**Question:**

**A particle executes the motion described by x(t) = x0 (1 – e-γt) where t ≥ 0, x0 > 0**

**(a) Where does the particles start and with what velocity?**

**(b) Find maximum and minimum values of x(t), v(t), a(t). Show that x(t) and a(t) increase with time and v(t) decreases with time.**

**Solution:**

(a) x(t) = x0 (1 – e-γt)

v(t) = dx(t)/dt = **+**x0 γ e-γt

a(t) = dv/dt = x0 γ2 e-γt

v(0) = x0 γ

(b) x(t) is minimum at t = 0 since t = 0 and [x(t)]min = 0

x(t) is maximum at t = ∞ since t = ∞ and [x(t)]max = e-γt = ∞

v(t) is maximum at t = 0 since t = 0 and v(0) = x0γ

v(t) is minimum at t = ∞ since t = ∞ and v(∞) = 0

a(t) is maximum at t = ∞ since t = ∞ and a(∞) = 0

a(t) is minimum at t = 0 since t = 0 and a(0) = -x0 γ2