B) Find the distance traveled by the particle P (x.y) between t = 0 and t 4 if the position at time t is given by: y = (2t + 1)i

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Q: Consider the curve given by 7(1) − (1²)7 + (t+ 1t³)3 + (t−11³) k a. Find the velocity, speed, and…

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Q: Find the coordinates at t = 0, π/4 , π of a particle moving along the path c(t) = (cos 2t,sin2 t).

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Q: Suppose that r(t) =. Then the speed is

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Q: Let x(t) = 3t, y(t) = 8t*. Then the slope of the tangent at t = 9 is O 12

A: The curve is defined by the following parametric equations xt = 3t ,  yt = 8t32 To evaluate : The…

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

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Q: Calculate the velocity, speed, and acceleration of the given paths. (a) x(t) = (t sin(t), t cos(t),…

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Q: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t > 0,

A: Solve

Q: (a) dy Given 4 sin 3x + 2exy = (2x + y)³, find dx'

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Q: Let 7 (t) = (2 – 5t2)i – (9t°)j – 4tk be the position of particle in space at time t. The %3D speed…

A: The speed of the particle at t=0 is 4

Q: The velocity and initial position are given. Find the position function. r(0) = (1, 2, 3) v(t) =…

A: Given that, initial position function r(0) =1, 2,3  and  v(t) =e3t, sint, 6t where v(t) is the…

Q: Q.2) Find the orthogonal trajectories of the family of curves e*(x sin y– y cos y) = c

A: 2 Given family of curves is e−xxsiny−ycosy=c. We have to find the orthogonal trajectories of the…

Q: A particle is moving back and forth on the x-axis. Its position at time t is s(t) = sin t + cos t.…

A: The position of the particle at time t is represented by the equation s(t)=sin t+cos t  ts(t)=sin…

Q: r(t) = 5 cos(t)i + 5 sen(t)j+3tk.

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Q: 9. Find the value g"(4) for the function g(t)= 31* +6t° +1.

A: The given equation is, gt=3t8+6t6+1

Q: 5. If s = t – 5t + 12t², find the velocity of the moving object when its accel- eration is zero.

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Q: - 9,0 <t < 5 Given the velocity in meters/second for v(t) = 3t – a.) find the displacement of the…

A: Solution is given below..