Let the velocity vector be v(t) = (4t°, –6 sin(3t) , 9 exp(3t)) and the initial position vector be r(0) = (2,3,0). Compute the position vector r(t).

The path r(t) = (t - sin t) i+ (1 - cos t) j describes motion on the cycloid x=t-sin t, y=1- cos t. Find the particle's velocity and acceleration vectors at t=, and sketch them as vectors on the curve. .....

The motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(12t - sin(12t))i + 4(1 − cos(12t))j Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = =

Consider the curve r(t) =(5t² − 3)i + (3t - sin(t))j. - y -5 v(t) = 5 -5 5 10 15 20 (a) Find the velocity of a particle moving along the curve. 25 X (b) Find the acceleration vector of a particle moving along the curve. a(t) =