Secure https session,masteringphysics.com 75141588 Phys 250 s2017 Prelecture Ch3

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Secure https session,masteringphysics.com 75141588 Phys 250 s2017 Prelecture Ch3 Uniform Circular Motion Part C Uniform Circular Motion Find the particle's velocity as a function of time. Learning Goal: Express your answer using unit vectors (e.gl A i+ B j, where A and Bare functions of w, R, t, and IT). To find the velocity and acceleration vectors for uniform circular motion and to recognize that this acceleration is the centripetal acceleration. Suppose that a particle's position is given by the following expression cos (wt)i sin(wt R cos (wt i sin (ut)j. Submit Hints My Answers Give Up Review Part Part D Find the speed of the particle at time t. Express your answer in terms of some or all of the variables w, R, and TT. Submit Hints My Answers Give Up Review Part incorrect; Try Again; 5 attempts remaining The correct answer does not depend on i, j, wt, wt. Part E Now find the acceleration of the particle. Express your answer using unit vectors (e.gl A it B j, where A and Bare functions of w, R, t, and IT). Signed in as JAEYEON PARK I Help Cose Resource previous l 9 of 9 l retum to assignment

Explanation / Answer

r(t) = Rcos(wt)i + R*sin(wt)j

v(t) = dr/dt

v(t) = R*-sin(wt)*wi + R*cos(wt)*wj

v(t) = -Rw*sin(wt)i + Rw*cos(wt)j    <<<<--------------answer

partD

speed = sqrt(vx^2+vy^2)

speed v = sqrt( (Rw*sin(wt))^2 + (Rw*cos(wt))^2 )

v = Rw*sqr( (sinwt)^2 + (coswt)^2)

V = Rw    <<<--------answer

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acceleration a(t) = dv/dt

a(t) = -Rw*cos(wt)*wi - R*w*sin(wt)w j

a(t) = -Rw^2*cos(wt)i - Rw^2*sin(wt)j

a(t) = -Rw^2*r(t)

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