Rectilinear Motion - Path Length

Path length is the total distance an object travels during its motion. It is a scalar quantity, meaning it has magnitude but no direction. Its dimensions are those of length (metres). For motion along a straight line, the path length accumulates for each segment travelled, regardless of direction. Path length differs from displacement, which depends only on the initial and final positions.

• Path length measures the actual distance covered by an object.
• It is always positive or zero and adds up every segment of motion.
• Displacement equals final position minus initial position and is a vector.
• When an object moves from x = 2 m to x = 5 m, path length = 3 m; displacement = +3 m.
• If it returns from x = 5 m to x = 4 m, path length = 3 m + 1 m = 4 m; displacement = 4 m – 2 m = +2 m.
• Moving next from x = 4 m to x = 1 m adds 3 m, so total path length = 4 m + 3 m = 7 m; displacement = 1 m – 2 m = –1 m.

• A person walking around a park may cover 2 km along the path, even if the straight-line distance between start and end is only 1 km.
• A delivery truck driving through city streets travels a longer route (path length) than the direct distance between its warehouse and the delivery point.
• A robot vacuum cleans every corner of a room, accumulating path length as it moves back and forth, while its displacement from start to end can be much smaller.