Mathematics

The key insight is that distance traveled along a path is arc length, not the straight-line displacement from the origin. You'll need to find the speed (magnitude of the velocity vector) using $\sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2}$, then integrate or use the fact that constant speed means distance = speed × time. Since the velocity components are constant here, the particle moves in a straight line at constant speed—making this much simpler than it first appears.

The key insight is that distance traveled along a path is arc length, not the straight-line displacement from the origin. You'll need to find the speed (magnitude of the velocity vector) using $\sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2}$, then integrate or use the fact that constant speed means distance = speed × time. Since the velocity components are constant here, the particle moves in a straight line at constant speed—making this much simpler than it first appears.