Four different objects are placed on a number line at 0. the chart describes the motion of each object. using the information in the chart, the distance and displacement of each object can be determined. which object has a distance that is three times as great as its displacement? w x y z

The chart with the information to answer this question may be found in other 's link, so I attach it now.

Explanation:

To facilitate the accompaniment of the reasoning, I copy the data here:

Object     Motion

  X           3 units left, 3 units right

  Y           6 units right, 18 units right

  W          8 units left, 24 units right

  Z          16 units right, 8 units left

The distance is the scalar magnitude that indicates the total length of the path traveled.

The displacement is the vector that indicates how far the end point and the initial point are.

In order to calculate the distance, the displacement and the ratio r = distance/displacement, to check which object has a distance that is three times as great as its displacement, i.e. r = 3, we use this new chart:

Object    Motion                                    Distance     Displacement  ratio

  X          3 units left, 3 units right        3 + 3 = 6       3 - 3 = 0            ∞

  Y          6 units right, 18 units right    6 + 18 = 24    6 + 18 = 24       1

  W         8 units left, 24 units right      8 + 24 = 32   -8 + 24 = 16     2

  Z          16 units right, 8 units left       16 + 8 = 24    16 - 8 = 8         3

The ratios were calculated dividing the distance by the displacement: distance / displacement.

For the object Z, that was 24 / 8 = 3. Thus, the object that has a distance that is three times as great as its displacement is the object Z.