The displacement (in metre) of a particle moving along x-axis is given by `x=18t +5t^(2). Calculate (i) the instantaneous velocity `t=2 s` (ii) average velocity between `t=2 s` to `t=3 s` (iii) instantaneous acceleration.

Explanation

` x =18t=5t^(2) `
(i) ` " "V=(dx)/(dt) =18 +10 t " "therefore " " V(t= 2s) =18+20 =38m//s`
(ii) Avg. Vel. `=("Displ.")/("Time") =(x(t=3)-x(t=2))/(3-2) =43 m//s `
(iii) ` a=(dv)/(dt) =10 m//s^(2) `