Mathematics

Problem

The coordinates of a particle moving in a plane are given by

x(t) = a \cos(pt)

and

y(t) = b \sin(pt)

where

a, b (< a)

and

p

are positive constants of appropriate dimensions. Then a. the path of the particle is an ellipse b. the velocity and acceleration of the particle are normal to each other at

t = \pi/(2p)

c. the acceleration of the particle is always directed towards a focus d. the distance travelled by the particle in time interval

t = 0

t = \pi/(2p)

a

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