(10 pts) The acceleration of an object is given by the vector function at) = (2,6t,...
The position vector r describes the path of an object moving in space. Position Vector r(t) = (cos(t), sin(t), 3t) t = 1 Time (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. a(T) = Submit Answer
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) (4t, 2 sin(t), cos(2t)) 5(0) (0, 5,5) r(t) Preview Preview Preview The position of an object at time t is given by the parametric equations Find the horizontal velocity, the vertical velocity, and the speed at the moment wheret - 4. Do not worry about units in this problem. Horizontal Velocity - Preview Vertical Velocity- Preview Preview peed- Find the position vector for...
The position vector r describes the path of an object moving in space. Position Vector Time r(t) = + i + tj + 2+ 3/2 t=9. (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) s(t) = a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. v9) al 9) =
Given information: An object is moving with velocity (in feet per second) described by the function v (t) = 4t + 1. We will reason about the object's position function, 8 (t). Question 1 How much does the position change over the time interval (0,4) Answer with a number only (units are feet) 36 Question 2 Question: Think back to the total change theorem. What additional Information would allow us to find a(4), the object's position at time t =...
(a) Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. a(t) - 13ti + etj + e-t, V(0) - k, r(0) = 1 + k r(t) -
5. (15 pts] A force acting on an object is proportional to the square root of the distance the object moves. The equation for the distance r is: 19 = kyr, for some constant k. The object starts at t=0 with position r = 0 and velocity v = 0. The object moves four meters in the first second. That is, r(t = 1) = 4. (a) Find the object's velocity as a function of position, v(r). (b) Find the...
The position vector r describes the path of an object moving in space. Position Vector Time r(t) = 12; + tj + 243/2k t = 4 (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. (4) = a(4) 11 Use the model for projectile motion, assuming there is no air resistance and g = 32 feet...
Question 4 An object has the velocity vector function v(t) (5, 4e4t, 6t + 2) and initial position 7(0) = (5,4, – 4) A) Find the vector equation for the object's position. F(t) B) Find the vector equation for the object's acceleration. alt) > Add Work Submit Question
(1 point) Given the acceleration vector a(t) = (-4 cos (2t))i + (-4 sin (2t))j + (-3t) k , an initial velocity of v (0) =i+ k, and an initial position of r (0)=i+j+ k, compute: A. The velocity vector v (t) = j+ . B. The position vector r(t) = j+ k
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) = (2+, 4 sin(t), cos(5t)) v(0) = (-3, -5,0) 7(0) = (-5,2, - 1) F(t)