If the position of a particle along Y axis is represented as a funtion of time t by the equation `y(t)=t^(3)` then find displacement of the particle during the period t to `t+Deltat`

Explanation

Position at time t is `y(t)=t^(3)`
Position at time `t+Delta t` is `y(t+Deltat)=(t+Deltat)^(3)`
`:.` displacement of the particle from to `t+Delta t` is
`y(t+Delta)-y(t)=(t+Deltat)^(3)-t^(3)`
`=t^(3)+3t^(2)Deltat+3t(Deltat)^(2)+(Deltat)^(3)-t^(3)`
`=3t^(2)Deltat+3t(Deltat)^(2)+(Deltat)^(3)`