Question

The slope at any point of a distance-time graph represents__________ ????

Answer 1

speed

Answer 2

Velocity,
the absolute value of velocity is speed

Answer 3

speed

Answer 4

The exact answer is instantaneous velocity.

Answer 5

If it is velocity I have a question. Say that the object which represent this graph has turned around and started to move backwards. Then the distance - time graph would still be increasing which means the slope of the graph can never be negative. But in this case the velocity should be negative. So I think it is not velocity it is the speed

Answer 6

speed

Answer 7

If you've ever taken a calculus-based physics course you'd understand that the answeris not speed since the slope also indicates a direction (positive or negative). Therefore, the slope of any point on a distance-time graph will always be the velocity at that point. As @ash236 stated, the absolute value of velocity is actually the speed. However, that's not what the question is asking.
In this case you have:\[Slope=\frac{Rise}{Run}=\frac{\Delta x}{\Delta t}=\frac{dX}{dT}\]
By definition:\[Velocity=\frac{dX}{dt}\]
@BAdhi: Look at the graph above. For your object to change directions it has to come to a stop at some point (where the horizontal). The graph then starts going negative when they start moving the opposite direction. Velocity as well as slope CAN be negative. The sign indicates the relative direction based on your chosen coordinate system.

http://www.physicsclassroom.com/class/1dkin/u1l3a.cfm
http://en.wikipedia.org/wiki/Velocity

Answer 8

We normally call the graph that Shane_B is mentioning, as displacement-time graph. I was referring to the graph where it shows the distance that it has traveled which cannot be negative (or decreasing), as distance-time graph. If kimmyg is mentioning about the graph that I've learnt as displacement - time graph I agree with Shane_B. But the resource below states the difference between two graphs

http://www.schoolingkids.com/india-ap-inter/physics-kinematics/study-notes/graphs-representing-motion-displacement-distance-time.php

Answer 9

That's a good point. What I drew was a displacement vs time graph which is what I'm more used to seeing. Looking again at the original question I see that the correct answer should be speed :)