Displacement/Distance Question?

Question

What is the difference between a displacement vs. time graph and a distance vs. time graph?

We did an experiment in physics where we dropped a ball and as it fell it marked a piece of paper 1/60s (60 times in a second) We circled every other dot created so we had two sets of data. (circled dots and non circled dots)

On the first set we measured the distance between each dot. (Dot one to dot three, then dot three to dot five, then dot five to dot seven, etc)

On the second set we started at dot one and measured how far it was to dot two. We then measured to dot four from dot one. Then from dot one to dot six and then dot one to dot eight, etc. (measuring how far from the release point basically)

So the first set of data is Displacement where the second set is distance. However, since they arent the same values, whats the difference between the displacement/time graph and the distance/time graph?

Thanks a lot.

Answer 1

If you run around a circle 1000 times and end up where you started from your displacement is 0. Your distance is 1000 times around the circle. Displacement is a vector quantity, distance is a scalar.

Answer 2

Seems to me that the distance/time graph is just what it says, the distance travelled by the ball in a certain amount of time (you should get a parabola).
The second graph, displacement/time, is of course similar to the other because it is also a distance plotted against time. Probably the use of this type of data is useful in calculating the instantaneous speed (or velocity) of the ball which is accelerating because it is falling. By comparing the distance travelled in the same time interval (I understand it is 2/60 ths of a second) you'll discover that the distance is increasing more and more in the same time interval, that is the ball is moving faster and faster, it's accelerating.
So the basic difference is that if you divide total distance by total time in the distance/time graph you are calculating an average velocity. Instead with the other graph you can derive another graph which is velocity/time (should be a linear curve, or better a line) which will tell you the instantaneous speed of the ball with time. Hope that's clear...but really distance and displacement are synonyms, what's important is the experiment and what you can deduce from it.

Answer 3

I would say in your case that what is being called displacement is the differential of distance: i.e. how much distance changes in a given interval. Distance is general, displacement refers to increments.

Distance = d
Displacement = ∆d

Answer 4

Displacement is the shortest distance between two points & its a vector quantity.Distance is scalar quantity & it can be the shortest distance or any distance betwen two points.