Math Problem Solver

A particle is moving in three dimensions. Its position vector is given by;

𝒓=2𝑥̂+(4+𝑡)𝑦̂−(2+3𝑡−3𝑡2)𝑧̂.

Distances are in metres and the time 𝑡 in seconds.

(i) What is the velocity vector at 𝑡=+5 ? [3]

(ii) Evaluate the speed in ms-1 at 𝑡=+5. [3]

(iii) Determine the acceleration vector and its magnitude in ms-2 at 𝑡=+5.