Question

Check my answer?
A railroad freight yard switch engine on a straight track travels 1000. m to the end of the track, then back 600. m, then forward 300. m.

a. What is the switch engine's final displacement from it's starting position?
I say 1900 because displacement is start to finish, and it went a total of 1900. m when you add all those up.
b. How far did it travel?
I say 700 m because 1000 - 600 is 400 then it went forward 300 so that's 700, meaning it traveled 700 m
Sorry I'm just confused on which is which. Did I get the two mixed up?

Answer 1

Unfortunately, you did. But not to worry!

Let's get some things clear first.

\[Displacement\]
To put it simply, displacement is the shortest distance between two points. Or in your question, this distance between the INITIAL POSITION of your object, and THE FINAL POSITION, irrespective of distance covered.

Let's break your question up into 3 parts.

1) Train travels 1000m forward.
2) Train travels 600m backwards.
3) Train travels 300m FORWARDS.

In Step 1 ) Your displacement would be a 1000m, since the distance b/w your start and end point is obviously a 1000m.

in Step 2) Your total displacement would be 400m. Why? Remember, displacement is IRRESPECTIVE of distance covered. The only thing that matters is the distance between your STARTING POINT, and your END POINT. The steps in it do not matter. If your starting point is at 0m, and if the train moves a 1000m forwards and then 600m backwards, it's 400m ahead of its starting point, right? That's displacement.

including Step 3) The train moves 300m forward. So now the distance between the starting point and the endpoint is.... yup, 700m.

Therefore your answer, is 700m.

Moving on to..

\[Distance\]

Distance is simple. It's just the TOTAL amount of distance the object covers, or HOW FAR it travels. So ..
\[1000+600+300 = 1900\]
Your total distance, milady, is 1900m. As simple as that.

\[Careful...\]
First of all, displacement is a vector. If your object ends up BEHIND or BEFORE the STARTING POINT, your displacement will be NEGATIVE. [Distance is a scalar, so signs do not matter in the quantity].

Secondly, if the question had stated "How far has object X travelled from THE STARTING POINT,", that's displacement. If it asks how far Object X has generally travelled, that's distance.

Hope my answer really helped you. If you have any confusions, feel free to message me about them. If you liked the answer, I'd appreciate if you hit the medal button, or became a fan. [Shameless advertising, I know].

Answer 2

To summarise.
\[a) 700m\]
\[b) 1900m\]

Answer 3

Thank you so much for helping me. This cleared it up very nicely for me. :)

Answer 4

Well, that's a relief. I'm glad to hear that. If you have any other questions, please don't hesitate to ask me. For now, mark this question as Closed, will you?