The path r(t) = (t - sin t) i - (1 - cos t) j describes motion on the cycloid x

Question

The path r(t) = (t - sin t) i - (1 - cos t) j describes motion on the cycloid x = t - sin t, y = 1 - cos t Find the particles velocity and acceleration vectors at t = 3pi/2, and sketch them as vectors on the curve. The velocity vector at t = 3pi/2 is v(3pi/2) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the Expression.) The acceleration vector at t = 3pi/2 is a(3pi/2) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the Expression.)

Explanation / Answer

r(t)=(t-sint)i+(1-cost)j

v(t)=r'(t)=(1-cost)i+(sint)j

a(t)=v'(t)=(sint)i+(cost)j

v(3pi/2)=r'(3pi/2)=(1-cos(3pi/2))i+(sin(3pi/2))j=1i-1j

a(3pi/2)=v'(3pi/2)=(sin(3pi/2))i+(cos(3pi/2))j =-1i +0j

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