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.

The total distance travelled by an object along its actual path, regardless of the direction of motion, is called path length.