The motion of a particle, along x-axis, follows the relation x = 8t-`3t^(2)` . Here x and t are expressed in metre and second respectively . Find (i) the average velocity of the particle in time interval 0 to 1 s and (ii) its instantaneous velocity at t = 1 s.

Explanation

(i) Let at = 0 , x = `x_(1)` and at t =1 , x = `x_(2)`.
`:. " " x_(1) = 8xx0-3xx0^(2) = 0`
and `" " x_(2) = 8xx1=3xx1^(2) = 5`m
`:.` Displacement `= x_(2)-x_(1) = 5`m and time taken is 1s.
`:.` Average velocity =` (5 m)/(1 s) = 5m. s^(-1)`.
(ii) Here instantaneous velocity,
`v = (dx)/(dt) = (d)/(dt)(8t-3t^(2)) = 8-2xx3t = 8-6t`
At t = 1 s, `(dx)/(dt) = 8-6xx1 = 2 m.s^(-1)`.