The position vector of an object at time t is given by: r = (at -31 )i+(6t² -bt)j Find the speed of the object at time t = 4.3 for a = 1.2 and b = 1.6 Give your result to three decimal places.

Q: A ball is thrown and at the time of release, the velocity of the ball is given by v = 22.6i + 8.2j,…

A: The initial velocity vector of the ball is given as, v=22.6i+8.2j in m/s The horizontal component of…

Q: or​ sphere, and show that the

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Q: r(t) = (sin 7t, t, cos t)

A: The vector equation is r(t)=sinπt, t, cosπt. Here, x=sinπt, y=t, z=cosπt Then x=sinπy, and z=cosπy…

Q: Find a unit vector that is parallel to the line tangent to the parabola y = x2 at the point (6, 36).

A: The parabola y = x2 and the point (6, 36)

Q: .3 At which point P does the curve r(t) = ( 2t have the tangent vector (24, -8, 3) ? (a) P(2, 2, 2)…

A: Here we have, the given curve is r→(t)=2t3, 2t2, 3t-1                now differentiate with respect…

Q: Q1: for the position vector cos³ (t)i + sin³ (t)j, 0<t</2. Find the vectors T, N, B and the length…

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Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: To indicate the direction in which t increases and sketch the graph of the vector function given…

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: Topic = vector

Q: Find the velocity vector for the position vector 7 (t) = (sin(7t), 6t°, e¯24).

A: Given,           The position vector is r→t=&lt;sin7t,6t9,e-2t&gt;.

Q: The position vector r of a moving particle at time t after the start of the motion is given by r…

A: The position vector r of a moving particle at time t after the start of the motion is given by r…

Q: (b) Suppose that the position vector of a particle moving in the plane is r-12vii+j, t>0. Find the…

A: This is application of derivative problem

Q: | The equation 7(t) = (8t) i + (8t – 5t²) j + (7) k gives the position of a particle in space at…

A: Differentiate wrt t for velocity and again differentiate wrt t for acceleration

Q: Find the velocity and acceleration vectors for the motion described by x = 6 + 4f², y= 6 + 4t², z =…

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Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

Q: Determine the velocity vector of the given path. c(t) = 9ti + 8t2j + 7t°k

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Q: A) What are the particle's coordinates when t =0? B) What are the particle's coordinates whent =2…

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Q: Find the velocity, acceleration, and speed of a particle with the position function 7(t) = ti+…

A: We have to find velocity and acceleration

Q: 2. If a particle's position is given by r(t) = <t ₁2 cost, sint), find the IN velocity,…

A: Given: particle position, r→t=t, 2 cos t, sin t We have to find the velocity, acceleration and speed…

Q: Q2. A point is moving along a curve whose position vector is Find : the acceleration components at /…

A: Consider the given position vector

Q: if the velocity function vector v = 3t 1+ tJ- 2k find the acceleration( a). -

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Q: Graph the curve traced by the given vector function r(t)=ti +2tj+costk;t>0.

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Q: Find the velocity and acceleration vectors in terms of u, and ug- de = 5t, where a is a constant r=a…

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Q: Determine the velocity vector of the given path. c(t) = 5ti + 3t?j + 6t³k

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Q: The path of a particle is moving in the plane with position vector . What is the speed of the…

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Q: Given the vector function 7(1)=(31²-1, 1-8√F³, 12t-4), find the speed & arc length of the curve on…

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Q: Assume that an object moves on a trajectory according to the equations x(t)=t+cost, y(t)=t−sint.…

A: An object moves on a trajectory according to the equations  Differentiating  with respect to t, we…

Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

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Q: A motion has R++) = (3.8m (347) 2² + (3 cos (3+));²³² + 3 +K A at time + -4 is. A vector dan gend to…

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Q: Determine the velocity vector of the given path. r(t) = (6 cos?(t), 3t – t3, 2t)

A: We have to find the velocity

Q: Find the velocity vector v(t) and the acceleration vector a(t) of the straight line motion given by…

A: Consider the given question,The velocity vector v(t) from the given position vector is find as,

Q: a) Find the speed of the particle at t = 3, and find the acceleration vector of the particle at t =…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: We have acceleration, initial velocity, and initial position, and if we integrate acceleration with…

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

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Q: Given differential of the function f at the point (3,2) 2. df = 3dr + ddy Find the directional…

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Q: 5) The position vector of a particle is given by s(t) = 3t2 – 4t + 5.Find the time at which the…

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Q: Q2) Find the vectors „N of the curve r(1) = ) at the point (1.1)

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Q: T The position vector r(t) = 4ti + 2tj+ t´k describes the path of an object moving in space. Find…

A: Given: rt=4ti^+2tj^+t26k^ To find the acceleration at of the object.

Q: 4 – Let the possition vector is given by 5tk r(t)* = sin3ti+ cost3j¬ + %3D Find a) The velocity b)…

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Q: Let r(t) = (15, cos t, -3 sint) be the position vector of an object. Find the velocity and speed of…

A: Given that rt=15,cost,-3sint  find the velocity and speed of the object

Q: For the position vector R(1) = e'i+e²ª j, the velocity at t=ln3 is:

A: Consider the given position vector: R→t=eti+29e2tj Find Velocity vector: Differentiate w.r.t "t",…

Q: 23. x = 1, y = 1/(1 + 1²),

A: Solution: The objective is to sketch the curve with the given vector equation

Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: Find the tangential and normal components of the acceleration vector for the curve 7(t) = (2t, 5t5,…

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Q: Q1: For the position vector r = et cos(t) i + et sin(t) j+ etk, find the velocity and acceleration…

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Q: A particle moving along a curve in the xy-plane has position (x(t), y(t)) = (-9 sin(9t), 3t² + 10t),…

A: Solved below

Q: Sketch the curve with the vector equation 7(t) = (t,2 – t, 2t). Indicate with an arrow the direction…

A: Solution

Q: The path r(t) = (t) i + (2t +5) j describes motion on the parabola y = 2x + 5. Find the particle's…

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Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: The given vector equation is

Q: (a) Find the position vector of a particle that has the given acceleration and the specified initial…

A: To find the position vector of a particle with given acceleration vector and initial conditions