Without findingT and N, write the acceleration of the motion r(t)=(cost+t sint)i+(sint-tcost)j, in the form a=a,T+aN. A BI -

Q: Given the vector function - r(t) = (t²- 4t)i + sin(2t − 4)3 + ( + ) Find the derivative of r(t). a)…

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Q: t3 Find the vector equation of the tangent line to 7(t) = 2 (e1-t) In t i+ tan-1 tj+ k at cos(t n)…

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

A: Given that: Acceleration, at=cost,5sint Initial position, x0,y0=3,0 Initial velocity, u0,v0=0,1 To…

Q: (d) § (Vx+sinx) dx

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Q: Let r(t) = (sin 3t +2t)i + (teʻ)j+(t° + 2t)k. Find the unit tangent vector at the point where t = 0.…

A: The unit tangent vector can be calculated using the differentiation. First obtain the derivative of…

Q: Find r'(t)'r" (t) given the following vector function. r(t) = 3cos(t)i+ 4sin(t)j cost sint -25cost…

A: Given vector function is, r(t)=3cost i+4sint j

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

Q: The normal component of the acceleration vector for an object with position vector r(t) = (cos(t),…

A: To check the given statement for True/False.The normal component of the acceleration vector for an…

Q: A projectile (such as a baseball or a cannonball) launched from the origin with an initial…

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Q: 4. Find the unit tangent vector T(t) for the vector function: r(t) = .

A: To find the unit tangent vector.

Q: If r(t) = −6ti + 4t²j – 8tk, compute the tangential and normal components of the acceleration…

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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: 2/3: The slope of the 4.8-kN force F is specified as shown in the figure. Identify the scalar…

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

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Q: Vrms= (um sin Wt dt 2 Vrms- sinwt)dt): %3D

A: To solve: Vrms=Vm22∫02πsin2ωtdt12

Q: Calculate the velocity and acceleration vectors, and speed for when t = Speed: 11. Velocity:…

A: To calculate the velocity and acceleration vectors, and speed for .