Trajectory
Trajectory is the path that a moving object follows through space. For example a tennis ball during the first service of top tennis players mostly circumscribe linear trajectory, while during the second service its trajectory is parabolically curved.
Distance travelled
Let us come back to our football pitch. Imagine that a midfielder gets the ball on the half-way line, dribbles past two defending players and passes the ball to his team-mate at the edge of the penalty area, as illustrated in Fig. 8. The football pitch is 100 m long.
Figure 8 Distance travelled (blue) and displacement (black) of a footballer.
The starting position of the midfielder in the Cartesian system of coordinates, with its origin in the corner flag to the left from the goal keeper, is (50 m, 24 m). His position in the moment of passing the ball is (16 m, 24 m). After measuring the trajectory we find out that the player ran for 52 m while dribbling past defending players but he only moved 34 m towards the goal. The length of the path he ran has little tactical importance in football because the resulting displacement towards the goal is what really counts. Distance travelled is a scalar physical quantity (i.e. it has no direction). The symbol used is s, the unit of measure is metre (m).
Displacement
Displacement is the shortest distance in the specific direction from the initial to the final position of a body’s motion.
Displacement is a vector with both the length and direction. In Fig. 8 the direction of displacement is marked with the black arrow and its length is 34 m. Displacement can be expressed graphically or numerically, as is the case in composition of forces. The unit of measure is metre (m) and the symbol used is d.