1.

5. [0/5 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 12.3.025.MI. MY NOTE Use the given acceleration function and initial conditions to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 7. a(t) = -cos ti - sin tj v(0) - j + k, r(0) = i v(t) = -sin (t )i + ( cost - 2 )j + k X r(t) = cos ti + (sin t - 2t )j + th X r(7) = cos ( 7 )i + (sin (7 ) - 14 )j + 7k X3. [0.83/5 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 12.3.007. 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 (3\\/2, 3V/2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = -6 sin (t) i + 6 cos(t)j X s(t) = 6 a(t) = -6 cos ( t ) i - 6 sin (t)j X (b) Evaluate the velocity vector and acceleration vector of the object at the given point. -3V2i+ 3v2j X -3V21 - 3V2j x (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.\f4. [1/5 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 12.3.016. The position vector r describes the path of an object moving in space. Position Vector Time r(t) = thi + tj + 2+3/2k t = 4 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = 2ti + j + 3V t k X s(t) = V 472 + 1+91 27 + 3 a(t) = .k 2V t X (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. V(4) = 8i + j + 6k X a(4) = 27 + | CO k X2. [0/10 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 15.1.012. Find | |FII. F(x, y) = yi + xj V ( 12 + x2 ) X Sketch several representative vectors in the vector field. y 4 X X 4 -2 2 4 -4 -21 4\f1. [0/10 Points] DETAILS PREVIOUS ANSWERS LARCALC Match the vector field with its graph. F(x, y) = xi + 3yj O O x 5 -5- XO O