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In Exercises 19−22, r(t) is the position of a particle in space at time t. Find the angle between the velocity and acceleration
19.
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University Calculus: Early Transcendentals (3rd Edition)
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Calculus: Early Transcendentals (3rd Edition)
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- If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. Find the acceleration vector. r(t) = (cos 3t)i + (2 sin t)j %3D O a = (-9 cos 3t)i + (-2 sin t)j O a = (-3 cos 3t)i + (2 sin t)j O a = (9 cos 3t)i + (-2 sin t)j O a = (-9 cos 3t)i + (-4 sin t)jarrow_forwardPlease solve thisarrow_forwardV(t)=?r(t)=?arrow_forward
- At time t = 0, a particle is located at the point (5,9,4). It travels in a straight line to the point (2,1,3), has speed 5 at (5,9,4) and constant acceleration - 3i-8j - k. Find an equation for the position vector r(t) of the particle at time t. The equation for the position vector r(t) of the particle at time t is r(t) = (Type exact answers, using radicals as needed.) i+ j+ k.arrow_forwardV(t)=?r(t)=?arrow_forwardA particle moves in the xy− plane according to the law x=at, y=bt2, where a>0, b>0. Determine the particle’s trajectory y(x) and sketch its graph. Determine the speed of the particle as a function of time. Find the angle ϕ between the velocity vector and the x−axis.arrow_forward
- Let r(t) (15, cos t, -3 sin t) be the position vector of an object. Find the velocity and speed of the object.arrow_forwardConsider the curve r(t) =(5t² − 3)i + (3t - sin(t))j. - y -5 v(t) = 5 -5 5 10 15 20 (a) Find the velocity of a particle moving along the curve. 25 X (b) Find the acceleration vector of a particle moving along the curve. a(t) =arrow_forwardPart 1.Given that the acceleration vector is a(t)=(−16cos(−4t))i+(−16sin(−4t))j+(3t)k the initial velocity is v(0)=i+k, and the initial position vector is r(0)=i+j+k, compute: A. The position vector r(t) B. The velocity vector v(t) Part2.Find the arclength of the curve r(t)=⟨72–√t,e7t,e−7t⟩r(t)=⟨72t,e7t,e−7t⟩, 0≤t≤1arrow_forward
- An object is moving in space with an acceleration 参数划分是指对负极 a(t) = -t i+3j+ (t – 3) k. Find the velocity vector v(t) and position vector r(t) of the object at any time t if at time t = 0, the object is at the point (0, 2. 1) and it has the velocity v(0) = i- j+ 2k. 问题的 极性问题是预期答享 于是和否的问题(因此 它们也称为是-否问 please ignore the background text Bartleby and solve black part only 极性问题可以是肯定的或否定的。 否定问题是非中性或有偏见的问题 “提问者偏向于基于原始信念的肯 定句答案或基arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 2 cos ti + 2 sin tj (VZ, V2) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. a(#) =arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage