Find the position vector for a particle with acceleration, initial velocity, and initial position given below. d(t) = (4t, 5 sin(t), cos(5t)) v(0) = ( – 1, 1, – 4) 7(0) = (– 5, 2, 2) 7(t) =
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- 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+kAn 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.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)=?
- Suppose we do not know the path of a hang glider, but only its acceleration vector a(t) = -(3 cos t)i - (3 sin t)j + 2k. We also know that initially (at time t = 0) the glider departed from the point (4, 0, 0) with velocity v(0) = 3j. Find the glider’s position as a function of 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 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.