Question

A particle moves in a straight line such that its displacement, x meters, from a fixed point O

on the line at time t seconds is given by 𝑥 = 60[𝑒

−2𝑡 − 𝑒

−4𝑡

].

(a) Find the time when the particle is instantaneously at rest.

(b) Find the displacement of the particle from O when t = 4 s.

(c) Find the total distance travelled during the first 4 seconds of its motion.

Answer 1

a)

$$2te^{-2t}=4te^{-4t}\\t=0\ s$$

b)

$$x=0.02\ m$$

c)

$$s=0.02\ m$$