Chapter 11.2, Problem 30E

The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3V2, 3V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. E) - =

Subtracting the two equations, find a vector equation for the curve of intersection between y= 4x2+(3/4)z2 and y-1= 3x2+(1/2)z2 for x>0. Find and simplify the tangential component of acceleration for your curve.

(14) The straight line L passes through the origin O and is in the direction i+mj. The straight line L' passes through the point A whose position vector is ai and is in the direction i+m'j. Write down the vector equations of L and L' and find the position vector of their point of intersection.

A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at time t = 0. The particle moves toward the point (3, 0, 3) with constant acceleration 2i + j + k. Find its position vector r(t) at time t.

The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the vector function F(t) = 5(24t - sin(24t))i +5(1 - cos(24t))j Find the velocity vector of the point. v(t) Find the acceleration vector of the point. ä(t) 2880 sin (24t)i + 2880 cos (24t)j✔ CABAME 120(1- cos (24t) )i + 120 sin (24t)j✔ Find the speed of the point. s(t) 240 sin (12t) wwwww Submit Question X Q Search EO H

the position vector r describes the path of an object moving in space. (a) Find the velocity vector, speed, and acceleration vector of the object. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. r(t) = ⟨t, −tan t, e^t⟩ t = 0

(6) The position vector of a particle is F = 4i-3j+ k, It is acted upon by a force F = 21-4j+8k. Find the Torque of the force about origin.

The vector describing a particular particle is given by T(t) = Rcos (wt)î + Rsin (wt) ĵ, where R and w are constants. (a) What is the magnitude of the position, |7|? What is its unit vector, f? (b) What is the velocity, ī, of this particle? What is it's magnitude, |0|? What is its unit vector, î? (c) What is the acceleration, a, of this particle? What is it's magnitude, Jā|? What is its unit vector, â? (d) Show that the acceleration points opposite to the position, ř° (i.e., â x -î), and determine the proportionality constant. |

How do you find the velocity and acceleration vectors at t=-1?