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In which of the cased from part c, if any, is the average velocity over an interval equal to the average of the constant velocities occurring in that interval? [For example, is
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- Mr. C is standing at the origin on the x-axis at position O. He starts from rest and accelerates at a rate of 2m/s/s [E] for 10s, then travels at a constant speed for 3 additional minutes, and then decides to accelerate at a rate of 1m/s/s[W] until he is travelling at a velocity of 5m/s[W]. Find the final position of Mr. C on the x-axis and the total time that he was in motion.arrow_forwardTwo masses hanging side by side from springs have positionss1 = 2 sin t and s2 = sin 2t, respectively. At what times in the interval 0 < t do the masses pass eachother?arrow_forwardIf a = (2, 0, 1), b = (0, 1, ½) and c = a × b, what is the magnitude of c?arrow_forward
- Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle θ above the horizontal at which it is thrown. Use the accompanying table and the equations below to estimate the partial derivatives. fx(x0,y0)= limΔx→0f(x0+Δx,y0)-f(x0,y0)Δx; fy(x0,y0) =limΔy→0f(x0,y0+Δy)-f(x0,y0)Δy Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer.(a) Estimate the partial derivative of r with respect to v when v=80ft/s and θ=45∘.arrow_forwardGive all a, b and c right solutions. A bullet was fired at a certain point A at an angle of 90 o from an inclined surface with slope of 5 vertical and 12 horizontal, and hit the surface at a distance of 70 m from point A measured along the inclined surface. a. What is the initial velocity(in m/s)? b. What is the maximum height (in m) reached by the bullet? c. What is the time (in sec) required for the bullet to hit the inclined plane?arrow_forwardThe derivative of the displacement r with respect to the time t is known to be:arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning