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(Solved): r(t)=(t-sint)i+(1-cost)j is the position of a particle in the xy- plane at t=\pi . Find the particle ...
r(t)=(t-sint)i+(1-cost)j is the position of a particle in the xy- plane at t=\pi .
Find the particle's velocity vector, speed, and acceleration vector at t=\pi .
r(t)=ti+tj+\sqrt(9-t^(2))k is the position of a particle in space at t=0. Find the
particle's velocity vector, speed, and acceleration vector at t=0. Next, find the
particle's direction of motion at t=0. Finally, write the particle's velocity at t=0
as the product of its speed and direction.
Find the parametric equations for the line that is tangent to r(t)=(cost+tsint)i
+(sint-tcost)j+tk at t=(\pi )/(2).
Evaluate the indefinite integral: \int (lnti+(1)/(t)j+k)dt.
Evaluate the integral: \int_1^(ln3) [te^(t)i+e^(t)j+(lnt)k]dt.
Solve the given initial value problem for r as a vector function of t .
(d^(2)r)/(dt^(2))=-4costj-3sintk,(dr)/(dt)|_(t)=0=3k and r(0)=4j
please answer all questions.