The motion of a particle in space is described by the vector equation ⃗r(t) = 〈sin...

The motion of a particle in space is described by the vector equation

⃗r(t) = 〈sin t, cos t, t〉

Identify the velocity and acceleration of the particle at (0,1,0) How far does the particle travel between t = 0 & t= pi

What's the curvature of the particle at (0,1,0) & Find the tangential and normal components of the acceleration particle at (0,1,0)

Expert Solution

milcah answered 2 years ago

The displacement of an object in simple harmonic motion is described by the equation 0.40m*sin(8.9rad/s(t)) +...

The displacement of an object in simple harmonic motion is described by the equation 0.40m*sin(8.9rad/s(t)) + 0.61m*cos(8.9rad/s(t)). A) Determine the position and velocity when t = 0 seconds. B) Determine the maximum displacement of the system. C) Determine the maximum acceleration of the system. D) Determine the velocity of the system at t = 6 seconds.

Let s(t)= ?? ? − ??? ? − ???? be the equation for a motion particle....

Let s(t)= ?? ? − ??? ? − ???? be the equation for a motion particle. Find: a. the function for velocity v(t). Explain. [10] b. where does the velocity equal zero? Explain. [20 ] c. the function for the acceleration of the particle [10] d. Using the example above explain the difference between average velocity and instantaneous velocity. (A Graph will be extremely helpful) [25] e. What condition of the function for the moving particle needs to be present...

The equation x(t) = A sin(ωt + φ) describes the simple harmonic motion of a block...

The equation x(t) = A sin(ωt + φ) describes the simple harmonic motion of a block attached to a spring with spring constant k = 20 N/m. At t = 0 s, x = 0.5 m and the block is at rest. a (5 points) After 0.5 s, the potential energy stored in the spring first reaches zero and the velocity of the block is in the negative x direction. What is the period of the oscillation? b (5 points)...

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , ,...

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , , ) B. The unit normal vector N=N= ( , , ) C. The unit binormal vector B=B= ( , , ) D. The curvature κ=κ=

Consider the vector function given below. r(t) = 2t, 3 cos(t), 3 sin(t) (a) Find the...

Consider the vector function given below. r(t) = 2t, 3 cos(t), 3 sin(t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) = N(t) = (b) Use this formula to find the curvature. κ(t) =

15. a. Find the unit tangent vector T(1) at time t=1 for the space curve r(t)=〈t3...

15. a. Find the unit tangent vector T(1) at time t=1 for the space curve r(t)=〈t3 +3t, t2 +1, 3t+4〉. b. Compute the length of the space curve r(t) = 〈sin t, t, cos t〉 with 0 ≤ t ≤ 6.

Determine whether the curve denoted by the vector function r(t) = <2 + sin(5t), -6, 3/2...

Determine whether the curve denoted by the vector function r(t) = <2 + sin(5t), -6, 3/2 (cos(5t))> lies on the surface 9x^2 - 36x - y^2 + 4z^2 = -36.

1.The position of a particle in rectilinear motion is given by s (t) = 3sen (t)...

1.The position of a particle in rectilinear motion is given by s (t) = 3sen (t) + t ^ 2 + 7. Find the speed of the particle when its acceleration is zero. 2.Approximate the area bounded by the graph of y = -x ^ 2 + x + 2, the y-axis, the x-axis, and the line x = 2. a) Using Reimmann sums with 4 subintervals and the extreme points on the right. b) Using Reimmann sums with 4...

Let C(R) be the vector space of continuous functions from R to R with the usual...

Let C(R) be the vector space of continuous functions from R to R with the usual addition and scalar multiplication. Determine if W is a subspace of C(R). Show algebraically and explain your answers thoroughly. a. W = C^n(R) = { f ∈ C(R) | f has a continuous nth derivative} b. W = {f ∈ C^2(R) | f''(x) + f(x) = 0} c. W = {f ∈ C(R) | f(-x) = f(x)}.

Consider the one-dimensional motion of a particle of mass ? in a space where uniform gravitational...

Consider the one-dimensional motion of a particle of mass ? in a space where uniform gravitational acceleration ? exists. Take the vertical axis ?. Using Heisenberg's equation of motion, find the position-dependent operators ? ? and momentum arithmetic operator ?? in Heisenberg display that depend on time. In addition, calculate ??, ?0, ??, ?0.

Question