Each of the four particles move along x axis. Their coordinates (in metres) as function of time (in seconds) are given by
`{:("Particle 1" : x(t)=3.5-2.7t^(3)" Particle 2" : x(t)=3.5+2.7t^(3)),("Particle 3" : x(t)=3.5+2.7t^(2)" Particle 4" : x(t)=3.5-3.4t-2.7t^(2)):}`
which of these particles is speeding up for `t gt 0` ?

Options

A. All four
B. only 1
C. only 1, 2 and 3
D. only 2, 3 and 4

Answer

A

Explanation

At t = 0
`(dx)/(dt)=0` for particles 1, 2 and 3 and `|(d^(2)x)/(dt^(2))|gt 0` for `t gt 0`
and `(dx)/(dt)=-3.4 m//s` for particle 4 and `(d^(2)x)/(dt^(2))` is negative for `t gt 0`
Therefore `t gt 0 , |(dx)/(dt)|` is increasing in all.