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A particle moves in a circle of radius r = 2.0 m. During the time interval from t = 1.5 s to t = 4.0 s its speed varies with time according to v(t) = C₁ C2 12³ : 4.0 m/s, c₂ = 6.0 m. s. C1 = What is the total acceleration of the particle at t = 2.0 s?

A particle moves in a circle of radius r = 2.0 m. During the time interval from t = 1.5 s to t = 4.0 s its speed varies with time according to v(t) = C₁ C2 12³ : 4.0 m/s, c₂ = 6.0 m. s. C1 = What is the total acceleration of the particle at t = 2.0 s?

College Physics
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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My understanding of the steps on this is stuck on a particular part. Please explain explicitly how we get 2c2/t^3 for aT.

Total Acceleration during Circular Motion A particle moves in a circle of radius r = 2.0 m. During the time interval from t = 1.5 s to t = 4.0 s its speed varies with time according to v(t) = C₁ Solution Centripetal acceleration is C2 What is the total acceleration of the particle at t = 2.0 s? Strategy We are given the speed of the particle and the radius of the circle, so we can calculate centripetal acceleration easily. The direction of the centripetal acceleration is toward the center of the circle. We find the magnitude of the tangential acceleration by taking the derivative with respect to time of v(t)| using Equation 4.31 and evaluating it at t = 2.0 s. We use this and the magnitude of the centripetal acceleration to find the total acceleration. 12³ ac = at = v(2.0s) = 4.0 U² C₁ = 4.0 m/s, C₂ = 6.0 m. s. r = 6.0 (2.0)² (2.5 m/s)² 2.0 m m/s = 2.5 m/s directed toward the center of the circle. Tangential acceleration is dv 2c2 dt 13 = = 3.1 m/s² 12.0 -m/s² = 1.5 m/s². 3 (2.0)³
Transcribed Image Text:Total Acceleration during Circular Motion A particle moves in a circle of radius r = 2.0 m. During the time interval from t = 1.5 s to t = 4.0 s its speed varies with time according to v(t) = C₁ Solution Centripetal acceleration is C2 What is the total acceleration of the particle at t = 2.0 s? Strategy We are given the speed of the particle and the radius of the circle, so we can calculate centripetal acceleration easily. The direction of the centripetal acceleration is toward the center of the circle. We find the magnitude of the tangential acceleration by taking the derivative with respect to time of v(t)| using Equation 4.31 and evaluating it at t = 2.0 s. We use this and the magnitude of the centripetal acceleration to find the total acceleration. 12³ ac = at = v(2.0s) = 4.0 U² C₁ = 4.0 m/s, C₂ = 6.0 m. s. r = 6.0 (2.0)² (2.5 m/s)² 2.0 m m/s = 2.5 m/s directed toward the center of the circle. Tangential acceleration is dv 2c2 dt 13 = = 3.1 m/s² 12.0 -m/s² = 1.5 m/s². 3 (2.0)³
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