1. If a particle moves in a plane so that its position is described by the function x = Acosùt, and y = Asinùt, it is

a.) moving with varying speed along a circle
b.) moving with constant speed along a circle
c.) moving with constant acceleration along a straight line
d.) moving along a parabola
e.) oscillating back and forth along a straight line

To determine the type of motion of the particle described by the given functions, we need to analyze the equations for the position of the particle.

The given equations for x and y are x = Acos(ωt) and y = Asin(ωt), where A represents the amplitude and ω represents the angular frequency.

Since the equations are trigonometric functions of time, they describe the circular motion of the particle. The x-coordinate represents the horizontal component of the particle's position, while the y-coordinate represents the vertical component.

By substituting values of time (t), we can visualize the path traced by the particle. Since the x and y coordinates are functions of the same angular frequency ωt, the path will be a circle.

Thus, the correct answer is b.) moving with constant speed along a circle.