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- The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(10t – sin(10t))ỉ + 3(1 – cos(104))} 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) =A charged particle begins at rest at the origin. Suddenly, a force causes the particleto accelerate according to the vector function a(t) = ⟨ sin(t) , 6t , 2cos(t)⟩Find functions for the velocity, speed and position of the particle at time tThe motion of a point on the circumference of a rolling wheel of radius 2 feet is described by the vector function r(t) = 2(23t sin (23t))i + 2(1 - cos(23t))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) =
- Find the direction in which the maximum rate of change occurs for the function f(x, y) = 4x sin(xy) at the point (1,5). Give your answer as a unit vector. (sin(5) + 5 cos(5))i + cos(15) i 1+ (5 cos (5))² + 10 sin(5) - cos (5) x Invalid notation. syntax incomplete.The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(22t – sin(22t))i + 3(1 – cos(22t))} Find the velocity vector of the point. v(t) = (66 – 66 cos(22t) )i + 66 sin( 22t)jv Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = 66y cos( 22t) + sin( 22t) xThe 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
- A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x - y, z + y + 6, z? ) and the net is decribed by the equation y = 1 – x - z', y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) · dS = IncorrectCompute the directional derivative of the function g(x,y) = sin (T(x - y)) at the point P(3, - 3) in the direction Be sure to use a unit vector for the direction vector. The directional derivative is (Type an exact answer, using t as needed.)Suppose that the vector-valued function F(t) < 3t, cos(5t), sin(5t) represents the position of an object at time t. Part a) Find a vector-valued function a(t) representing the object's acceleration at time t. Part b) What is the distance travelled by the object between time t = 0 and time t 1?
- Compute the directional derivative of the function g(x.y)= sin (T(4x - 6y)) at the point P(-3,1) in the direction Be sure to use a unit vector for the direction vector. The directional derivative is (Type an exact answer, using a as neededA net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)Let u(t) = 21'i+ (-1)j-8k. Compute the derivative of the following function. (11 +7t) u(t) Select the corect choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function O B. The derivative is the vector-valued function Di+ i+ k. Click to select and enter your answer(s) and then click Check Answer
