Consider a particle moving rectilinearly according to x = 13 - 312 -45t m, where t is in sec. Draw the x-t, v-t and a-t curves for the interval 0 sts8 sec. Determine the distance travelled during the first 8 seconds.

Q: Consider a particle moving rectilinearly according to x = t3 - 3t2 -45t m, where t is in sec. Draw…

A: Here is the solution of the given problem.

Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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Q: Find orthogonal trajectory to the curve given by r = a(1 + cos θ)

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Q: Find the length of the curve y = V4t2 – 1 dt, 1<x<2 O 3 O 8 O 104 3. O 15

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Q: Which of the following functions parametrizes the portion of the curve x=y³-4 that starts at (-4,0)…

A: In this question , we can check one by one all option .

Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: Find the arc length of the curve y 1 on the interval [1, 2]. %3D 4x2

A: Given:    y = x4/8 + 1/4x2   Interval : [ 1 , 2 ]

Q: . Sketch the curve parametrized by r(t) = (ltl + t, ltl - t)

A: The given curve is rt=t+t, t-t. Sketch the graph of the above curve as shown below.

Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

Q: Find the distance between the point (-2m, 0, -m) and the tangent line of the curve ū(t)= (me* – }i--…

A: Given: u-(t)=(met2-t)2i-4mt+1j+t-mt2+1k at t=0 First we will find tangent line of the curve…

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: Find a parametrization for the curve described below. the line segment with endpoints (5 - 1) and…

A: Given point :( 5 , -1 ) (10 , -6 )

Q: Find Sc F · dr for F = 3yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Find the arclength of the curve over the given interval. (a) r = 1 + sin θ, 0 ≤ θ ≤ 2π

A: Given: The curve is: r=1+sinθ over the interval 0≤θ≤2π The objective is to find the arclength of the…

Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

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Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

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Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

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Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/3 In (2 + v 2 ) – - In (1)

A: Since you have posted 2 questions we will solve one for you please resubmit the question. Given:…

Q: Graph the curve. x = 5et cos(t), y = 5e' sin(t), 0stsn y y 50 10 40 -120 100 -80 -60 -40 - 20 -10 20…

A: We have to graph the curve and find its exact length.

Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

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Q: * Find the length of the curve.7 (ähäs 3) f(x) = In(sec x) %3D 4 In(3 + 1) O In(3 + 2) O In(2 + 2) O…

A: Hence option (d) is correct.

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

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Q: x = sin´t, y = cosʻt, 0<t<3™

A: Given x=sin2t, y=cos2t, 0≤t≤3π

Q: If x = 8cos3theta and y = 8sin3theta, find the total length of the curve swept out by the point…

A:

Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: Find the curva tuie For He Curve 2+); +(6 cos 2t) + 5¢ K %3D

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Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: he length of the curve y = sin(3X) from x = 0 to I= is given by

A:

Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

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Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: Calculate the arclength of the following curve on the given interval. y%=2x3/2+1O on the interval…

A:

Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

Q: ind the equation of the tangent line to right branch of the hyperbola == sec t, y= tant, 2 - sts at…

A: Topic:- application of derivatives

Q: Calculate the arc :length of the curve y = In(2x + 1) over the interval

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Q: Let C be the closed curve starting at (0, 1) traveling along the parabola y = (x – 1)? up to the…

A: Using Green's Theorem we solve the above question.