Two soccer players kick a soccer ball back and forth along a straight line. The first player kicks the ball 11 m to the right to the second player. The second player kicks the ball to the left weakly; it only moves 2.7 m before stopping. (Consider the right to be the positive direction. Where applicable, indicate the direction with the sign of your answer.) (a) What is the total distance that the ball moved?
m
(b) At the end, what is the displacement of the ball (from the first player)?
m

a) 13.7 m

b) 8.3 m

Explanation:

a)

The total distance traveled by the ball is just the sum of the distances traveled after being kicked by the first player (11 m.)  plus the distance moved after being kicked by the second player (2.7 m), independent of the direction of  the movement:

       

b)

The total displacement of the ball, is just the difference between the final and initial position, by definition.If we choose the origin to be in the place that the ball is kicked by the first player,

       

The final position along the x-axis, is just the distance traveled to the right (11 m) minus the distance traveled to the left (considering the right to be the positive direction), 2.7 m:

       

      ⇒ Δx = xf - x₀ = 8.3 m  - 0 m =  8.3 m