If the position of a particle is given by x(t) = 12 t^2 - t^3, where x is in meters and t is in seconds, find the position of the particle when the particle's acceleration is zero? * O - 8 m +8 m + (8 m) i - (8 m) i None of the above

If the position of a particle is given by x(t) = 12 t^2 - t^3, where x is in meters and t is in seconds, find the position of the particle when the particle's acceleration is zero? * O - 8 m +8 m + (8 m) i - (8 m) i None of the above

Name: 8.If the position of a particle is given by x(t) = 12 t^2 – t^3, wher
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Description: 8.If the position of a particle is given by x(t) = 12 t^2 – t^3, where x is in meters and t is inseconds, find the position of the particle when the particle's acceleration is zero? *%3D-8 m+8 mO + (8 m) iO - (8 m) iO None of the above

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter3: Two-dimensional Kinematics

Section: Chapter Questions

Problem 65PE: An athlete crosses a 25-m-wide river by swimming perpendicular to the water current at a speed of...

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You have a great job working at a major league baseball stadium for the summer! At this stadium, the speed of every pitch is measured using a radar gun aimed at the pitcher by an operator behind home plate. The operator has so much experience with this job that he has perfected a technique by which he can make each measurement at the exact instant at which the ball leaves the pitchers hand. Your supervisor asks you to construct an algorithm that will provide the speed of the ball as it crosses home plate, 18.3 m from the pitcher, based on the measured speed vi of the ball as it leaves the pitchers hand. The speed at home plate will be lower due to the resistive force of the air on the baseball. The vertical motion of the ball is small, so, to a good approximation, we can consider only the horizontal motion of the ball. You begin to develop your algorithm by applying the particle under a net force to the baseball in the horizontal direction. A pitch is measured to have a speed of 40.2 m/s as it leaves the pitchers hand. You need to tell your supervisor how fast it was traveling as it crossed home plate. (Hint: Use the chain rule to express acceleration in terms of a derivative with respect to x, and then solve a differential equation for v to find an expression for the speed of the baseball as a function of its position. The function will involve an exponential. Also make use of Table 6.1.)
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Unreasonable Results Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth. (a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity? (c) Is there a problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height? (d) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.
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1 - Two pieces of furniture move according to the following position functions: x1(t)=0.5t3−5t2+6t+4x1(t)=0.5t3−5t2+6t+4 x2(t)=t2−3t+3x2(t)=t2−3t+3 c) Determine at what instants (t>0) the two rovers intersect (use WolframCloud or another application to solve the equation generated in this item. Code example for WolframCloud below - shift+Enter to execute the code, Enter only skips a line). Demonstrate obtaining the equation in the appendix by hand. d) Present, in one of the annexes, an image of the graph of the two position functions plotted on the same diagram. e) Is the direction of the velocities of the furniture the same or is it opposite in the two instants in which the furniture occupies the same position? demonstrate your reasoning
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27-30 - Circular Motion The position of an object in circular motion is modeled by the given parametric equations. Describe the path of the object by stating the radius of the circle, the posi- tion at time t = 0, the orientation of the motion (clockwise or counterclockwise), and the time that it takes to complete one revolution around the circle. 27. x = 3 cos 1, y = 3 sin t 28. x = 2 sin t, y = 2 cos t 29. x = sin 21, y = cos 21 30. x = 4 cos 31, y = 4 sin 31