The displacement of particle moving along x-axis is given by `x=6t+12t^(2)`, calculate the instantaneous velocity at `t=0 and t=2s.`

Explanation

Displacement of a particle `=6t+12t^(2)`
Differentiate with respect to 't'
`x=6t+12dt^(2)`
`(dx)/(dt)=6+24t" "[because x^(n)=nx^(n-1)]`
`because" The instantaneous velocity "v_(i)=(dx)/(dt)=6+24t.`
Instantancous velocity at t = 0 ,
`v_(i)=u+at=6+24(0)`
`v_(i)=6m//s`.
Instantancous velocity at `t=2s`.
`v_(i)=u+at=6+24(2)=6+48`
`v_(i)=54ms^(-1)`