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 (b

Question

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 (b < a) and p are positive constants of appropriate dimensions. Then

G1 Physics · Accepted Answer

Eliminating t from x = a cos(pt) and y = b sin(pt) gives x²/a² + y²/b² = 1, so the path is an ellipse. Also a⃗ = -p²r⃗, so acceleration is directed toward the origin (the centre of the ellipse). At t = π/(2p), velocity is along the -x direction and acceleration along the -y direction, hence they are perpendicular. The distance travelled from (a,0) to (0,b) is one-quarter of the ellipse, not a. Therefore A and B are certainly correct. The printed source also marks C, but its wording says 'focus'…

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 (b &lt; a) and p are positive constants of appropriate dimensions. Then

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 (b < a) and p are positive constants of appropriate dimensions. Then