Question

if the position of a particle along Y axis is represented as a function of time t by the equation Y(t)=t^3 , then find displacement of the particle during period t to t+ ∆t​

Answer 1

Answer:

3t²Δt + 3t(Δt)² + (Δt³)

Explanation:

Position  at time is y(t) = t³

position at time t + Δt is y(t + Δt) = (t + Δt)³

therefore, displacement of the particle during the period from t to t + Δt

is y(t + Δt) - y(t) = (t + Δt)³ - t³

= t³ + 3t²Δt + 3t(Δt)² + (Δt)³ - t³

= 3t²Δt + 3t(Δt)² + (Δt³)