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Position-Time Graphs - Numerical Analysis - help3

Distance is a direction-ignorant quantity that describes how much ground an object covers. Displacement is a direction-aware quantity that describes how far out of place an object is. Reading coordinates off a position-time graph allows one to determine the distance and the displacement.

There are four very similar versions of this question. Each version provides a position-time graph of a two-stage motion and asks the learner to either determine the displacement for the entire motion. Two of the versions are shown below.

Version 1
This position-time graph describes an object's motion. Use it to determine the overall displacement (in m) of the object during the 10.0 seconds of motion. Enter the appropriate + or – sign.

Version 2
This position-time graph describes an object's motion. Use it to determine the overall displacement (in m) of the object during the 10.0 seconds of motion. Enter the appropriate + or – sign.

Displacement refers to how far out of place an object is at the end of the motion relative to the beginning of the motion. It is the overall change in position of the object. Displacement is a vector quantity; that is, a direction-conscious quantity. If an object moves one direction and later changes its direction to move another direction, then that direction change has an impact upon the displacement.

In this question, the object first moves in the positive direction away from the starting position. At a certain time the person is a maximum distance from the starting position and then turns around and walks back towards the starting position to some final position. To determine the displacement, you will need to read the position coordinate for the starting position (t= 0.0 seconds) and for the final position (end of graph). Then find the change in these two positions. That involves subtraction.

Because displacement is a vector, it has a direction. Usually directions are adjectives like right or left or east or west. But graphs represent these adjectives with positive and negative values. So your answer could be positive or negative. Determining which sign to use is easy. Just subtract the initial position from the final position to get the change in position. (Incidentally, that's how you always calculate a change. ) If the result is negative, then enter a negative answer.

Displacement = Final Position - Initial Position

Try the link below to our Tutorial for more information:

Distance and Displacement