Suppose a car is travelling through a bend in a road that can be described by the hyperbola y = + 20 m when x is in meters. Additionally, when you know that when x = 100 m, the km km car is travelling at a speed of 40 and its speed is increasing at a rate of 8,000. Find: a) What is the radius of curvature of the road at the location x = 100 m? b) What are the normal and tangential acceleration of the car at this point? c) What is the magnitude of the car's acceleration? d) Bonus: If the car's x-position is increasing, what is its acceleration in Cartesian coordinates?
Suppose a car is travelling through a bend in a road that can be described by the hyperbola y = + 20 m when x is in meters. Additionally, when you know that when x = 100 m, the km km car is travelling at a speed of 40 and its speed is increasing at a rate of 8,000. Find: a) What is the radius of curvature of the road at the location x = 100 m? b) What are the normal and tangential acceleration of the car at this point? c) What is the magnitude of the car's acceleration? d) Bonus: If the car's x-position is increasing, what is its acceleration in Cartesian coordinates?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Angular speed, acceleration and displacement
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Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
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