Kinematics: Find average speed from displacement-time graph.

[NoahCygnus]

Homework Statement

The problem is as follows;
A boy begins to walk eastward along a street infront of his house and the graph of his displacement from the house is shown in the figure. His average speed for the whole time interval is equal to?
https://scontent.fdel3-1.fna.fbcdn.net/v/t31.0-8/fr/cp0/e15/q65/17311005_704452213062233_4909110252429640342_o.jpg?efg=eyJpIjoidCJ9&oh=1c9f0cc2b2f56cd9f19c2586e956db44&oe=59697593

Homework Equations

Average speed = total distance / total time

The Attempt at a Solution

First of all, I'm confused about how to find speed from a displacement time graph. It should be rather distance time graph. Even if I find the total distance traveled by the boy from displacement graph and divide it by the total time , my answer doesn't match that given in the book.

Here's what I tried :
First I found the total distance traveled by the boy , which came out be 120 m , then divided it by 20 seconds. the answer I got was 6 m/s. But in the book , the answer is 2 m/s. I'm confused. even if I find velocity , which is displacement over time , it'll come out to be 0 , as total displacement is 0. Please rectify me if I'm wrong somewhere.

 

[mjc123]

The time is in minutes, not seconds. But I get 6 m/min, so I'm doing it the same way as you. I can't see how the book gets 2 m/s.

 

[PeroK]

First of all, I'm confused about how to find speed from a displacement time graph. It should be rather distance time graph.

Okay, let's say I agree. So, can you turn a displacement to time graph into a total-distance to time graph?

 

[BvU]

Hello Noah,

There must be something wrong with the book answer. Time is clearly indicated in minutes. Is he crawling ?
And the numbers don't fit either. My money is on your result !

 

[NoahCygnus]

The time is in minutes, not seconds. But I get 6 m/min, so I'm doing it the same way as you. I can't see how the book gets 2 m/s.

Yes metre/minutes , pardon I got the unit for time wrong.

 

[NoahCygnus]

Okay, let's say I agree. So, can you turn a displacement to time graph into a total-distance to time graph?

I don't know if you can , but considering its one dimensional motion I'd say yes. That's the assumption I made. I simply added all the displacements of the graph and neglected the signs.

 

[BvU]

I also resent the way the 'book' (?) abuses the term displacement. What does it mean that the displacement from the house is minus 20 m at t = 15 min ?

 

[PeroK]

I don't know if you can , but considering its one dimensional motion I'd say yes. That's the assumption I made. I simply added all the displacements of the graph and neglected the signs.

I think you actually did it already. You didn't draw a graph, but you did split the graph into sections where he was going in different directions - and that gave you the total distance.

In general, some questions will give you all the information you need in the format you need it. Other questions will give you all the information you need, but not necessarily in the simplest fomat. You have to be confident to deal with that.

Note, also, that outside your studies in the real world there's no guarantee you do have all the information. Sometimes part of problem solving is working out what is missing and going and getting it! But, I digress.

I would assume the book has a typo and move on.

 

[NoahCygnus]

Hello Noah,

There must be something wrong with the book answer. Time is clearly indicated in minutes. Is he crawling ?
And the numbers don't fit either. My money is on your result !

I checked the step by step solution for this problem;
https://scontent.fdel3-1.fna.fbcdn.net/v/t31.0-8/fr/cp0/e15/q65/17240588_704461776394610_5421162738994608245_o.jpg?efg=eyJpIjoidCJ9&oh=b3ff7cbf87b1a7df3304502934b9373c&oe=5964EB0C
I don't get it.

 

[PeroK]

I checked the step by step solution for this problem;
https://scontent.fdel3-1.fna.fbcdn.net/v/t31.0-8/fr/cp0/e15/q65/17240588_704461776394610_5421162738994608245_o.jpg?efg=eyJpIjoidCJ9&oh=b3ff7cbf87b1a7df3304502934b9373c&oe=5964EB0C
I don't get it.

You need a new book. That is all rubbish!

 

[NoahCygnus]

I think you actually did it already. You didn't draw a graph, but you did split the graph into sections where he was going in different directions - and that gave you the total distance.

In general, some questions will give you all the information you need in the format you need it. Other questions will give you all the information you need, but not necessarily in the simplest fomat. You have to be confident to deal with that.

Note, also, that outside your studies in the real world there's no guarantee you do have all the information. Sometimes part of problem solving is working out what is missing and going and getting it! But, I digress.

I would assume the book has a typo and move on.

So

You need a new book. That is all rubbish!

Right. The author is high on weed.