he position vector r describes the path of an object moving in space. Find the velocity v(t), speed s(t), and acceleration a(t) of the object. r(t) = 4ti + 4tj + 2tk (t) = (t)

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A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

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A: For the given position vector  r(t) = ti + (-t2+9)j  Velocity, Speed, acceleration vector is…

Q: The position vector r describes the path of an object moving in space. Position Vector Time r(t) =…

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Q: The position vector r(t) = 5ti+2tj+4tk describes the path of an object moving in space. Find the…

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

A: Given,           The position vector is r→t=<sin7t,6t9,e-2t>.

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Q: Q2) Find the vectors the curve r(t) = at the point (11) of

A: First of all find r'(t) and the length of r'(t). Here, r'(t)=<2t,2t2,1> |r'(t)|=4t2+4t4+1…

Q: The position vector r(t) = t2i + tj + 2t3 2k describes the path of an object moving in space . (a)…

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

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Q: The motion of a vibrating particle is defined by the position vector r = 10(1 - e-35i + (4e 2sin…

A: We will use here  d(u.v)= u d(v)+v.d(u) Which is know as derivative formula for product.

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A: v(t)=∫at dt =∫1,4 dt=t,4t+Cwhere C is the constant vector ie, C=2,5 which is obtained from the…

Q: C:r=r(t)=(1+t,2 – 3t, 4t)

A: We Have :— X = 1 + t Y = 2 — 3t Z = 4t

Q: The position vector r(t) = ti + 5tj + 3tk describes the path of an object moving in space. (a) Find…

A: Given: The position vector r(t) = ti + 5tj + 3tk,

Q: Given the vector function ř(t) = (– 3t, 5t°, 2t° + 3) Find the velocity and acceleration vectors at…

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Q: |A particle starts at the origin with initial velocity i – j+ 3k. Its acceleration is ã(t) = 6t ỉ +…

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Q: The position vector r describes the path of an object moving in space. Position Vector Time r(t) =…

A: We have to find  the velocity  vector  , speed and acceleration  vector.

Q: An object moves in space with acceleration a(t) = 12t²i+6tj+2k. When t = 0, the object is at (1, 0,…

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Q: Ex:- Find the directional derivative of fOxy,2) =X-xy-7 atRC,1,0) in the direction of vector A=21-33…

A: Solution is given below:

Q: Given an acceleration vector, initial velocity (uo,vo), and initial position (xo.yo), find the…

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Q: The position vector r describes the path of an object moving in space. Position Vector Time r(t) =…

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Q: The position vector r describes the path of an object moving in space. Position Vector Time 1 r(t):…

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: Given : r(t) = t2i + tj  Point : ( 4,2)

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.

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Q: Given the vector function 7 (t) = (3t, 5t", – 3t° + 2) - Find the velocity and acceleration vectors…

A: Given that vector function r→ t=3t,5t2,-3t5+2 To find the velocity and acceleration at t=-1Solution…

Q: The position vector r(t) = 4ti + 4tj − 2tk describes the path of an object moving in space . (a)…

A: (a) Consider the provided position vector, rt=4ti+4tj -2tk Find the velocity vector, speed, and…

Q: Given the vector function F(t) = (5t, - 3t², − 4t³ + 5) Find the velocity and acceleration vectors…

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Q: The points A and B have position vectors j+2k and 2i+j-2k respectively. (i) Find a vector equation…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: The vector r(t) is the position vector of a particle at time t. Find the angle between the velocity…

A: we have position vector,  r→(t)=(4t2+8)i+(2t3-5t)k

Q: The position vector r describes the path of an object moving in space. Position Vector Time r(t) =…

A: Given r(t)=ti+5tj+3t2k

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A: Given, r→(t)=2t, t5, -3t4+4

Q: Suppose the position vector of a particle in space at time t is given by: r (12t,-312,-8t/2) (a)…

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Q: The position vector r describes the path of an object moving in space. Position Vector Time r(t) =…

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Q: 6. The position vector r = (4t, t³, –t) describes the path of an object moving in space. Find the…

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Q: sketch the curve represented by the vector-valued function and give the orientation of the curve.…

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Q: Qe A Find the Vector 5 unit length in the direction of vector perpendicular to the lane which passes…

A: We have to find the normal vector first.

Q: The equation r(t) = i+ 16t j is the position of a particle in space at time t. Find the angle…

A: r(t)=32t i+12t-16t2 jVelocity vector v(t) = drdt=32 i+12-32t j

Q: Find the positive t when the vector r(t) = (7t, 6t², 9t2 3) is perpendicular to r'(t). - t =

A: NOTE: Refresh your page if you can't see any equations. . take derivative