1. Consider the path of a moving object described by 7(t) = (cos? t, sin? t,t) -25 sts 2 (a) Find v(t) and i (). (b) Find T(t) and T (-). (c) Find the speed at t =
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- A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t sin 2t. Find the speed of the particle when t = /2.Find the coordinates at t = 0, π/4 , π of a particle moving along the path c(t) = (cos 2t,sin2 t).Find orthogonal trajectory to the curve given by r = a(1 + cos θ)
- Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0, 2π] .Which option gives the correct parametric representation of this path? A. x(t) = sin (2(pi)t), y(t) = cos (2(pi)t), 0 ≤ t ≤ 2 B. x(t) = sin ((pi)t), y(t) = cos ((pi)t), 0 ≤ t ≤ 2 C. x(t) = sin ((pi)t), y(t) = cos ((pi)t), 0 ≤ t ≤ 1 D. x(t) = sin (2(pi)t), y(t) = cos (2(pi)t), 0 ≤ t ≤ 1Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is the radius? how many times is it transversed? And in what direction?