A particle moves in the plane for 0≤t≤4 seconds with velocity vector
v(t)=⟨3t2−2,4cost⟩ (meters per second).
At t=0 the particle is at position r(0)=⟨5,−1⟩ meters.
(a) Derive an explicit expression for the position vector r(t) for 0≤t≤4. Show all steps in your derivation.
(b) Determine the particle’s position at t=4 seconds.
(c) Compute the displacement vector of the particle over the interval 0≤t≤4 seconds.
(d) Evaluate the total distance traveled by the particle on 0≤t≤4. Express your answer to three decimal places and include appropriate units.