8) Find the position vector r(t) for a particle with acceleration a(t) = (5t, 5 sint, cos 6t), initial velocity (0) = (3,-3, 1) and initial position r(0) = (5,0,-2).
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- The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(10t – sin(10t))ỉ + 3(1 – cos(104))} Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) Find the speed of the point. s(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?The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(22t – sin(22t))i + 3(1 – cos(22t))} Find the velocity vector of the point. v(t) = (66 – 66 cos(22t) )i + 66 sin( 22t)jv Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = 66y cos( 22t) + sin( 22t) x
- A bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 seconds. Where is the bee located at time t = 6 if [°r' (Use symbolic notation and fractions where needed.) r' (u) du = 0 location:The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the vector function F(t) = 5(12t - sin(12t))? +5(1 cos(12t))) Find the velocity vector of the point. (t) = 60(1- cos (12t)i + sin(12t)j) × Find the acceleration vector of the point. ä(t) = 720(sin(12t)i + cos (12t)j) ✓ Find the speed of the point. s(t) = 120 sin (6t) (Write i, j, k for 2,5, k.) Submit QuestionThe motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function F(t) = 4(26t – sin(26t))i + 4(1 – cos(26t))3 Find the velocity vector of the point. ü(t) = | 4(26 – 26 cos(26t))i + 4(26 sin( 26t ))j Find the acceleration vector of the point. ä(t) = | 2704 sin(26t )i + 2704 cos( 26t)j v| Find the speed of the point. s(t) = 2704 sin(26t)i+ 2704 cos( 26t)j x syntax error. Check your variables - you might be using an incorrect one.
- 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 (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 charged particle begins at rest at the origin. Suddenly, a force causes the particleto accelerate according to the vector function a(t) = ⟨ sin(t) , 6t , 2cos(t)⟩Find functions for the velocity, speed and position of the particle at time t
- particle moves along a path with velocity (t) = sin(t) i + t³j + etk. ts) Find its acceleration. Suppose the particle's initial position is P(2,1,-1). Find the particle'sThe motion of a point on the circumference of a rolling wheel of radius 2 feet is described by the vector function r(t) = 2(23t sin (23t))i + 2(1 - cos(23t))j - Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) =If r(t) = cos(7t)i + sin(7t)j – 3tk, compute the tangential and normal components of the acceleration vector. COS Tangential component ar(t) Normal component an(t) =