: [a, b] particle's traject ory is described by y. (2 log(t), tt1). Suppose a Problem...
A particle's trajectory is described by = (}t - 2t2) m and y 2)m, where t is ins. Part A You may want to review (Pages 81 - 85) What is the particle's speed at t = 0s? v 2 m/s Previous Answers Submit Correct Here we learn how to determine the speed at a given time from the expressions for components of a trajectory. Part B What is the particle's speed at t = 4.5s? Express your answer using...
5, (25 points 4 pages max) Suppose that γ(t) = (x(t), y(t)) is a smooth (infinitely differentiable) plane curve. For curves such that lh'(t) 0, the (signed) curvature is defined to be the quantity K(t) (a) Suppose the curve γ(t) is the graph of a function, ie x(t)-t and y(t) f(t) for some function f. Write the formula for the curve in this case. Suppose you were at a critical point of the graph of f. What does the curvature...
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Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
all a,b,c,d
1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on C with gradient Vg, we define the normal derivative Dng by and we define the Laplacian, V2g, of g by For this problem, assume D and C satisfy the hypotheses of Green's Theorem and the appropriate partial derivatives of f...