Find the position vector for a particle with acceleration, initial velocity, and initial position given below. ä(t) = 3tỉ + 3 sin(t)J + cos(4t)k v(0) = – 47 – 43 – 2k F(0) = 47 + 33 – 3k F(t) +
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- Find 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)=?16) (a) Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. (b) Use a computer to graph the path of the particle. a(t)=ti+e^tj+e^-tk, v(0)=k, r(0)=j+kA 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?
- 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 1find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-tFind the position vector for a particle with acceleration, initial velocity, and initial position given below a(t)= r(0)= r(t)=?
- The rocket is launched at timet = 0withr (0)=2i-6j+4k. If the initial velocity of the rocketisv (0)=4i+1j+10kand acceleration of the rocket at the time ? is given bya(0)= t2+ t cos t j+16e-4t k , then find the vector functionr(t), which describes the rockettrajectoryFind the position vector of a particle that has the given acceleration and the specified initial velocity and position: a(t) = 19t i + et j + e−t k, v(0)=k, r(0)= j + kfind the velocity and acceleration vectors in terms ofur and uθ . r = a(1 - cos θ) and dθ/dt = 3
- An object moves with an acceleration vector: a(t) = - 3 Cos(t) i - 3 Sin(t) j + 2k If initially the object starts from the point (3,0,0), with a speed v(0)=3j , find: The position r(t) of the object for all time t and the normal and tangential components of acceleration.11.Find the position and velocity vectors of a particle that has the given acceleration and the given initial velocity and position: a(t) = 4i- 72j+ (72t + 4)k, v(0) = i+ k and r(0) = j+ 3k.Find the acceleration of the particle at t = 0 with the position function r(t)=e6ti+e8tj