Beginner · 9 min
Distance and displacement
Distinguish the length of a route from the change in position.
A route and a change of position
Distance is the total length of the path travelled. It is a scalar and does not include direction. Displacement is the change from starting position to finishing position and includes direction. For motion along one line, choose a positive direction and use signs. Returning to the starting point gives zero displacement even though the distance travelled can be large.
Worked example
A walker moves 7 m east and then 3 m west. Distance = 7 + 3 = 10 m Displacement = 7 − 3 = 4 m east
Two different averages
Average speed is total distance divided by total time. Average velocity is displacement divided by total time. Use the entire time interval, including stops. These averages can differ. A runner completing a lap has nonzero average speed but zero average velocity over the complete lap because the final position equals the initial position.
Worked example
A person walks 10 m out and 10 m back in 20 s. Average speed = 20 ÷ 20 = 1 m/s Average velocity = 0 ÷ 20 = 0 m/s
Describe an out-and-back route
- Draw a route of 8 m north followed by 8 m south. Find its distance and displacement.
- If the whole trip takes 16 s, calculate average speed and average velocity. State which answer includes direction.