What is the magnitude of the final velocity for a particle initially moving with velocity 0.4 m/s and subjected to perpendicular acceleration 0.15 m/s² for 2 seconds?

When a particle moves at 0.4 m/s and experiences acceleration of 0.15 m/s² at right angles to its velocity for 2 seconds, velocity components combine vectorially. The initial velocity vector v₀ = 0.4 m/s stays constant in one direction, while acceleration changes velocity perpendicular by a × t = 0.15 × 2 = 0.3 m/s. The final velocity magnitude is found using Pythagoras theorem where vf = square root of ((0.4)² + (0.3)²) = square root of (0.16 + 0.09) = square root of 0.25 = 0.5 m/s. This illustrates orthogonal components in motion and is a classic problem reflecting vector addition in kinematics vital for students learning motion analysis. The perpendicular nature of the acceleration means the original velocity component remains unchanged while a new perpendicular component is added, creating a resultant velocity that can be calculated using basic trigonometry and vector principles fundamental to understanding two-dimensional motion problems.