Kinematics: Find average speed from displacement-time graph.

In summary, the problem is that the author is confused about how to find speed from a displacement time graph. He tries to do it using distance time graph instead, but gets incorrect results.
  • #1
NoahCygnus
96
2

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.
 
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  • #2
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.
 
  • #3
NoahCygnus said:
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?
 
  • #4
Hello Noah, :welcome:

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 ! :smile:
 
  • #5
mjc123 said:
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.
 
  • #6
PeroK said:
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.
 
  • #7
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 ?
 
  • #8
NoahCygnus said:
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.
 
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Likes NoahCygnus
  • #9
BvU said:
Hello Noah, :welcome:

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 ! :smile:

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.
 
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  • #10
NoahCygnus said:
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!
 
Last edited by a moderator:
  • #11
PeroK said:
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
PeroK said:
You need a new book. That is all rubbish!
Right. The author is high on weed.
 

Related to Kinematics: Find average speed from displacement-time graph.

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.

2. How is average speed calculated from a displacement-time graph?

The average speed is calculated by dividing the total distance traveled by the total time taken. In a displacement-time graph, the slope of the line represents the average speed.

3. What is the difference between speed and velocity?

Speed is the rate at which an object moves, while velocity is the rate at which an object moves in a specific direction. Velocity takes into account both the speed and direction of an object.

4. Can the average speed change during the motion of an object?

Yes, the average speed can change if the object is moving at varying speeds. The average speed is calculated by taking the total distance traveled divided by the total time taken, so any changes in speed will affect the average speed.

5. How can we use kinematics to analyze real-world situations?

Kinematics can be used to analyze real-world situations by using mathematical equations and graphs to describe the motion of objects. By understanding the principles of kinematics, we can predict an object's future position, speed, and acceleration.

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