Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) = (3t, 2 sin(t), cos(6t)) v(0) = (- 4, 2, 0) 7(0) = (-5, - 2, - 1) F(t) =
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- The equation for the position vector r(t) of the particle at time t isFind the position vector for the particle with acceleration, initial velocity, and initial postion given below. a(t)= <5t,3sin(t), cos(3t) v(0)= <3,0,-2>r(0)= <0,5,-2>r(t)=?A particle is moving with velocity V(t) = ( pi cos (pi t), 3t2+ 1) m/s for 0 ≤ t ≤ 10 seconds. Given that the position of the particle at time t = 2s is r(2) = (3, -2), the position vector of the particle at t is?
- Find the position vector for a particle with acceleration, initial velocity, and initial position given below a(t)= r(0)= r(t)=?Find the position vector of a particle that has the following acceleration, initial velocity, and initial position. a(t) = 2t i + sin(t) j + cos (2t) k v(0) = i r(0) = -j Thank you.find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t
- A particle at (1, 0, 0) starts moving in space in such a way that its position vector at any time t ≥ 0 is R~ (t) = (cost + tsin t)ˆi + (sin t − t cost)ˆj + t 2ˆk, t ≥ 0.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 vectors at time t = 0.find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)
- give the position vectors of particles moving alongvarious curves in the xy-plane. In each case, find the particle’s velocityand acceleration vectors at the stated times, and sketch them asvectors on the curve. Motion on the parabola y = x2 + 1r(t) = ti + (t2 + 1)j; t = -1, 0, and 1Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ, cos θ, cos 3θ〉, θ = π/3