The figure shows the path of a particle that moves with position
(a) Draw a vector that represents the average velocity of the particle over the time interval
(b) Draw a vector that represents the average velocity over the time interval
(c) Write an expression for the velocity vector
(d) Draw an approximation to the vector
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Chapter 13 Solutions
Calculus 8th Edition
- (1n |t – 1], e', vî ) 1. Let 7(t) = (a) Express the vector valued function in parametric form. (b) Find the domain of the function. (c) Find the first derivative of the function. (d) Find T(2). (e) Find the vector equation of the tangent line to the curve when t=2. 2. Complete all parts: (a) Find the equation of the curve of intersection of the surfaces y = x? and z = x3 (b) What is the name of the resulting curve of intersection? (c) Find the equation for B the unit binormal vector to the curve when t= 1. Hint: Instead of using the usual formula for B note that the unit binormal vector is orthogonal to 7 '(t) and 7"(t). In fact, an alternate formula for this vector is ア'(t) × ア"(t) ア(t) ×デ"(t)| B(t) =arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = ti + (-t2 + 8)j (1, 7) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. v(1) = a(1)arrow_forwardA car travels in a straight line for 1 hour. Its velocity v in miles per hour at six-minute intervals is shown in the table. (a) Produce a reasonable graph of the velocity function v by graphing these points and connecting them with a smooth curve. (b) Find the open intervals over which the acceleration a is positive. (c) Find the average acceleration of the car (in miles per hour per hour) over the interval [0, 0.4]. (d) Approximate the acceleration at t = 0.8.arrow_forward
- A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at time t = 0. The particle moves toward the point (3, 0, 3) with constant acceleration 2i + j + k. Find its position vector r(t) at time t.arrow_forwardFind the velocity vector v(t), given the acceleration vector a(t) = (3e¹, 7, 10t +9) and the initial velocity v(0) = (8,-5,3). (Use symbolic notation and fractions where needed. Give your answer in the vector form.) v(t) = 2(e' - 2)i + (3t-2)j + (3r² +9r+2)k Incorrectarrow_forwardA baseball is hit 3 feet above the ground at 110 feet per second and at an angle of 45° with respect to the ground. (a) Find the vector-valued function for the path of the baseball. r(t)= 55 2t, 55 2t-16t², 3 x (b) Find the maximum height. (Round your answer to three decimal places.) 97.530 x ft (c) Find the range. (Round your answer to one decimal place.) ft (d) Find the arc lengths of the trajectory. (Round your answer to one decimal place.) S = ftarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning