The relation between the time taken and the displacement of a moving body is s = `2t - 3t^(2) + 4t^(3)`, where the unit of s is in metre and that of t is in second. Find out the displacement, velocity and acceleration of the body 2s after initiation of the journey.

Explanation

Here, s = 2t - `3t^(2) + 4t^(3)`
`:.` In 2 s the displacement of the body is,
s `= (2xx2) - [ 3xx(2)^(2)] + [4xx(2)^(3)]`
= (4-12+32) = 24 m
Now the velocity is,
`v = (ds)/(dt) = 2 - 6t+12t^(2)`
`:.` After 2 s,
`v = 2-(6xx2) + [12xx(2)^(2)] = 38 "m.s"^(-1)`
Again the acceleration is,
`a = (dv)/(dt) = -6 +24t`
`:.` Acceleration after 2 s,
`a = -6+24 xx2 = -6+48 = 42 "m.s"^(-2).`