Question

Give example of a motion where ` x gt 0, vlt 0, agt ` at a particular instant.

Answer 1

Let the motion is represented by
`x(t) = A + Be^(-gammat)`
Let `A gt B` and `gamma gt 0`
Now velocity `x(t) = (dx)/(dt) = -Bgammae^(-gammat)`
Acceleration `a(t) = (dx)/(dT) = Bgamma^(2)e^(-gammat)`
Suppose we are considering any instant t, then from Eq. (i) , we can say that
`x(t) gt 0, v(t) lt 0` and `a gt 0`