Find a parametrization of the motion starting at A(1,2,3) at time t= 4 and finishing at...
Find a parametrization of the circle of radius 4 in the xy-plane, centered at (−2,−4), oriented counterclockwise. The point (2,−4) should correspond to t=0. Use t as the parameter for all of your answers.
Find a parametrization of the tangent line at the point indicated. r(t) = (1 - 4, 4t, 5t), t = 2
what is the answer for number 4 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
Name that Parametrization 4. (a) Consider these two sets of parametric cquations: x(1)-1 y(t) = sin t 0<t<oo x (t) sin t y(t) = t 0<t<00 What is the difference between their associated curves? (b) Given any set of equations of the form What does the graph of the set of equations y(r) = 1 x(!) = f (1) 0<t<oo look like? Use a calculator to check that f(x) = x5-3x3 + 5x + 2 is one-to-one. 5, (a) (b)...
Understand how to find the equation of motion of a particle undergoing uniform circular motion. Consider a particle--the small red block in the figure--that is constrained to move in a circle of radius R. We can specify its position solely by θ(t), the angle that the vector from the origin to the block makes with our chosen reference axis at time t. Following the standard conventions we measure θ(t) in the counterclockwise direction from the positive x axis. (Figure 1)...
Whats the answer to number 1? 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j + ick)...
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) = 3e-4t a. Compute the Wronskian of these two vectors. Wx(t) = (67 – 33t+27)e-4t), b. On which intervals are the vectors linearly independent? If there is more than one interval, enter a comma-separated list of intervals. The vectors are linearly independent on the interval(s): (-infinity,1),(1,4.5),(4.5, infinity), help (intervals). c. Find a matrix P(t) = (Pu(t) P12(t)) so that 21 and 22 are fundamental solutions...
(1 point) Find the velocity v(t) and speed || v(t) || of a particle whose motion is described by r = 7, y = 2+3 – 9+, 2= {2 – 67 +9 v(t) || v(t)||
(1 point) Suppose the position of a particle in motion at time t is given by the vector parametric equation r(t) = (3/t - 2), 7, 2+3 – 6t). (a) Find the velocity of the particle at time t. v(t) = (b) Find the speed of the particle at time t. Speed = (c) Find the time(s) when the particle is stationary. If there is more than one correct answer, enter your answers as a comma separated list. t =
The acceleration of a particle in one dimensional motion at time t is given by at t () 6 2 = − . Given that the initial velocity of the particle is 0, find the average velocity of this particle over the first 4 seconds. Please solve and show work. Thank you so much!