Suppose that the acceleration vector is a(t) = (e²t + 2t, e²t – 3,0) and also that the velocity vector at t = 0 is v(0) = (3/2, 1⁄2, 0) 7 and the position vector at t = 0 5 9 is r(0) = ( 21, 22, 0). 4 Find r(t).
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- A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at time t = 0. The particle moves to-ward the point (3, 0, 3) with constant acceleration 2i + j + k. Find its position vector r(t) at time t.At time t = 0, a particle is located at the point (1, 2, 3). (Vector Functions) It travels in a straight line to the point (4, 1, 4), has speed 2 at (1, 2,3) and constant acceleration 3i – j+k. Find equation for the position vector r(t) of the particle at time 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?
- At time t = 0, a particle is located at the point (1, 2, 3). It travels in a straight line to the point (4, 1, 4), has speed 2 at (1, 2, 3) and constant acceleration 3i - j + k. Find an equation for the posi-tion vector r(t) of the particle at time t.At time t = 0, a particle is located at the point (4,8,6). It travels in a straight line to the point (1,7,2), has speed 2 at (4,8,6) and constant acceleration - 3i -j- 4k. Find an equation for the position vector r(t) of the particle at time t.Find the velocity and acceleration vectors of the particle whose position at time t seconds is given by s= (t',t, (3t – 1)³) at the instant that t =1. If distances are measured in meters, what is the speed of the particle at this time?
- At time t = 0, a particle is located at the point (8,4,7). It travels in a straight line to the point (3,9,6), has speed 3 at (8,4,7) and constant acceleration negative 5i + 5 j - k. Find an equation for the position vector r(t) of the particle at time t.Find the velocity and acceleration vectors in terms of u, and ug- de r=a cos 20 and dt = 5t, where a is a constant (- 10at sin 20 ) u, + ( 5at cos 20 ) ue y = - a cos (20) • (4 + 5t)) u, + (5a( cos (20) – 4t sin (20)) ue a =At time t=0, a particle is located at the point (3,9,4). It travels in a straight line to the point (7,8,6), has speed 6 at (3,9,4) and constant acceleration 4i-j+2k. Find an equation for the position vector r(t) of the particle at time t -O+¹+* The equation for the position vector r(t) of the particle at time t is r(t) = (Type exact answers, using radicals as needed.)
- 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.8) Find the position vector r(t) for a particle with acceleration a(t) = (5t, 5 sin t, cos 6t), initial velocity (0) = (3, -3, 1) and initial position (0) = (5, 0, -2).Given the vector function r(t) = (2t, t,- 3t +4) Find the velocity and acceleration vectors at t= 1. (-1) = al- 1) =