When describing how an object moves, the first concepts to understand are displacement and velocity. Study them while paying attention to the difference between distance and speed.
Basic Knowledge
Displacement is the directed amount of motion from the starting point to the ending point (a vector quantity). In contrast, distance is the scalar quantity representing the actual path traveled. For example, if you travel 100 m away and return, the distance is 200 m, but the displacement is 0 m.
Velocity is the vector quantity obtained by dividing displacement by time:velocity v = displacement Δx ÷ time Δt
In contrast, speed is the scalar quantity distance ÷ time.
Average velocity means displacement ÷ time over a given interval, while instantaneous velocity means displacement ÷ time over an extremely short interval (the slope of an x-t graph).
In SI units, the unit of velocity is m/s. Conversion from the everyday unit km/h is 1 m/s = 3.6 km/h.
Displacement (a directed line segment from the starting point to the ending point; a vector with direction and magnitude)
Velocity (displacement ÷ time; a vector quantity with direction)
Speed (distance ÷ time; a scalar quantity without direction)
Average velocity (total displacement over an interval ÷ time)
Instantaneous velocity (the slope of the tangent to an x-t graph)
Scalar/vector (a quantity without direction / a quantity with direction)
Further Study (Background and Significance)
In physics, the same numerical value often has different meanings. “Speed 60 km/h” and “velocity 60 km/h eastward” contain different amounts of information. By distinguishing vectors and scalars, we can accurately describe complicated motion such as projectile motion and circular motion.
In an x-t graph (position-time graph), the slope of the graph represents velocity. A straight line means uniform linear motion, while a curve means that velocity is changing. The slope of the tangent at one point is the instantaneous velocity.
In the 17th century, Galileo Galilei expressed speed numerically and established a method for describing motion mathematically. Before this, Aristotle’s incorrect claim that “heavier objects fall faster” dominated, but Galileo’s experiments and mathematical descriptions overturned it.
- Displacement = directed quantity (vector); distance = path length (scalar).
- Velocity = displacement/time (vector); speed = distance/time (scalar).
- The slope of an x-t graph = velocity.
- 1 m/s = 3.6 km/h.
- Instantaneous velocity = the slope of the tangent to an x-t graph.
- On a round trip, displacement = 0 but distance ≠ 0.
- SI unit: m/s.
Points to Note (Common Confusions)
① Displacement (a vector) and distance (a scalar) are different. When an object returns in the opposite direction, displacement becomes smaller while distance continues to increase. ② Do not confuse velocity (a vector) with speed (a scalar). If a problem says “include the direction in your answer,” find the velocity. ③ Average velocity is displacement ÷ time and does not necessarily equal “the average of the initial and final velocities” (although they are equal in uniformly accelerated motion).
Practice
- An object moves 600 m east and then returns 200 m west. Give its displacement and distance traveled.
- Find the average velocity (m/s) of an object that travels 80 m in 10 seconds.
- Convert a velocity of 90 km/h to m/s.