Consider the position vector of a particle for 0≤t≤3 given by
r(t)=⟨t2−4t,3t−t3⟩.
Respond to the following.
(a) Determine the velocity vector v(t) and the acceleration vector a(t).
(b) Find all times in the interval 0≤t≤3 at which the velocity and acceleration vectors are perpendicular. Give exact values or justify any numerical approximations.
(c) Decide whether the particle’s speed is increasing or decreasing at t=1.5. Show all work leading to your conclusion.