The coordinates of a particle moving in a plane are given by and where and are…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The coordinates of a particle moving in a plane are given by x(t)=acos⁡(pt)x(t) = a \cos(pt) and y(t)=bsin⁡(pt)y(t) = b \sin(pt) where a,b(<a)a, b (< a) and pp are positive constants of appropriate dimensions. Then (1) the path of the particle is an ellipse (2) the velocity and acceleration of the particle are normal to each other at t=π/(2p)t = \pi/(2p) (3) the acceleration of the particle is always directed towards a focus (4) the distance travelled by the particle in time interval t=0t = 0 to t=π/(2p)t = \pi/(2p) is aa

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