4. If a particle moves in the xy-plane so that at time t its position vector is sin 31 ,3r2 find the velocity vector at time t= - 2

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A: The path is given as,r(t)=<t2,t3> So, the velocity and acceleration will be, respectively,…

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Q: 6. A particle moves in the xy-plane in such a way that its velocity vector is (1+1, 1). If the…

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Q: 6: Find the work done by the force F = -7y i+ 10x j along one loop of the curver = sin 70 (in the…

A: Given

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A: Given  a t=4t,5 sint, cos 3twe know that,v→t=∫a t dt +C1r t=∫vt  dt  +C2 ∴v→t=∫4t, 5 sint, cos 3t…

Q: Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ,…

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Q: A bee with velocity vector r' (t) starts out at (3, –5, –2) at t = 0 and flies around for 3 seconds.…

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Q: Suppose that a particle follows the path r(t) = 2 cos(3t)i+ jsin(3r) – ť² k. Determine the velocity…

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Q: 1. Suppose that r(t) = (3 cos(3t) t,3 sin(3t), 5t). a. Determine the velocity, the acceleration and…

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A: For the solution follow the next steps.

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Q: 3. A unit vector tangent to the curve y x2 at the point (2, 4).

A: We are entitled to solve only one question at a time so we will answer only the first question.…

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Q: An object rotates with angular acceleration, a, defined as dw a = dt where w is the angular…

A: Solving two ordinary differential equations, we get the result.

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Q: 10. A particle moves in the xy-plane so that the position of the particle is given by x(1) =1+cos t…

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Q: For time t > 0, the position of a particle moving in the xy-plane is given by the vector (, et).…

A: Position of particle = (1/t, e3t) Velocity = derivative of position of particle = (-1/t2 , 3e3t)

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A: Velocity is equal to the first derivative of position vector   Let x =f1t and y =f2t then velocity…

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A: We can answer first question as per the honor policy. Please resubmit other parts as well to know…

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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: 2. The position vector of the particle is 1 R = î cos(t) + 3 sin(t) + k log (0 <t < n/2). sin t' (a)…

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Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j +…

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Q: Example 4. Find the tangent vector at the point (2,4). on the top half of the circle x² + y² = 1…

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A: Explained below

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Q: 1. Find the tangent vector to the curve 6t r(t) = [t° – t, (2t + 1)*] at t = 1.

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Q: C) If R(t) = (In(t2 + 1)i + (tan-t)j + (VE +1)k, is the position vector of a particle at time (t).…

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