i Q4. (a). Consider the vector function f(t) = (t2,2t + Int) on the interval [1,...
The equation of motion of a particle is described by: OM t-1+(2)1 Determine the equation of trajectory of the particle and plot it on an xy coordinate system. a) b) At which point the motion starts. c) Determine the velocity vector and the acceleration vector of the particle in function of t d) Determine the tangential acceleration, the normal acceleration, and the radius of curvature in function of t. Is this a central acceleration, why or why not? At what...
7.(16 points) Consider the curve F(t) = 4 cos(t)ī + 4 sin(t); +3tk. (a) Find the unit tangent vector T(t) and the unit normal vector function Ñ (t) at the point (-4,0,37). (b) Compute the curvature k at the point (-4,0,31).
1) For this problem use the following space curve: F(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
a © lt (t) =<et, zee, 2t> a) compute the are arclength of the from tuoto tl. b) Reparemeterize the respect to *length. c) compute Ť, š, and B. F with d) Find formula for the curvature Evaluate it at t:1. e) Find the normal and osculating planes at t:1. f) Find the tangential and normal components of the acceleration t:1.
For the curve defined by find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at r(t)-<C-t cos(t), e'sin(t) > We were unable to transcribe this image3.4 Motion in Space Due Sun 05/19/2019 11:59 pm Hide Question Information Questions Find Components of the Acceleration Q4 11/1] For the curve defined by r(t)-(e-t cos(t), e'sin(t)〉 C Q 8 (0/1) find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at t - Q 10 (0/1)...
8.) (13 pts.) Assume that curve C is given parametrically by F(t) = ($(t)) i + (g(t)) ; + (h(t)) k for t20. Let s = s(t) be the arc length of curve C from t = 0 to t. Assume that the unit tangent vector is given by 1 S T(t) = T(t(s)) = + V5+ sa 5 + s2 Find the curvature of C when the arc length is s = 2. v6+ 2 75 5 + 32
We will all rate if correct 1) For this problem use the following space curve: F(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the plot of the curve? IV 20 50 (a) Compute the arc length of the curve from t = 0 to t = 3. (b) Find the unit tangent vector T(t). (c) Compute the curvature of the curve at any value of t. 12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the...
9. + 4/12 points Previous Answers SCalcET8 13.3.019. Consider the following vector function. r(t) = (3V2t, et, e-3) (a) Find the unit tangent and unit normal vectors T(t) and N(t). t(c) = V2(V2c3! -e-31 N(t) = (b) Use this formula to find the curvature. k(t) = Need Help? Read it Watch It Talk to a Tutor O Type here to search N e 9
Using Mathematica Consider the vector-valued function r(t)=et cos t i+(sin t)/(t+4) j +t k. a) Plot the curve with t going over the interval [-2, 2]. b) Plot the curve again over the same interval, but this time add the velocity vector in blue at (1, 0, 0) to the graph. c) Plot the curve again over the same interval, along with the blue velocity vector at (1, 0, 0), but this time add the acceleration vector in red at...