There are two coloured pencils: red and blue. The tip of the red pencil is ng the x-axis and the tip of the blue pencil is moving along the y-axis. The the tips of the red and blue pencils at time t are given by differentiable t) and b(t), respectively. We know that r(t) = sin(t) – 2. However, we know e tip of the blue pencil moves along the positive y-axis with b(0) = b'(0) = 1. %3D

Find T, N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t = 0 Give your answers to two decimal places T (0) = Ń (0) = B(0) =

9. The velocity function for a particle moving through space is given by v(t) = sec² (@t) tan¹5 (ot). Find the T position function, s(t) for the particle given that s = 0. (Note: @is a constant. Do not convert to sines and cosines. Must 4@ show the steps to find the constant "c".)

5. The position function of a moving object is given by 7(t) = (, et", cos t). Find its velocity COS and acceleration functions.