distance time graphs like this one here allow us to visualize how far something has traveled in a certain period of time for example this one here could represent the journey of a cyclist as well as telling us that she's travelled a total of 50 meters in 11 seconds graphs like this also tell us a lot about the different parts of the journey and you need to be able to interpret each of these different stages the most important thing to know is that the gradient of the line at any point tells you the speed that the object is traveling at that time this is because the gradient is equal to the change in distance divided by the change in time which remember is the formula for speed so just remember that on a distance time graph the gradient is always equal to the speed so for this first section where she travels 20 meters in two seconds the gradient would be 20 divided by two so 10 meters per second and as it's a straight line her speed must have been constant through this period meanwhile a flat line like this one in the middle tells us that he's stationary as the gradient and so the speed are both zero which means that she's not moving at all if the line then gets steeper the gradient and speed must be increasing and so this part shows acceleration while a decreasing gradient shows deceleration now one really important point is that while the speed is constantly changing like it is in these last two stages it's a bit trickier to find the speed at any particular point because we can't just take a total of the entire period like we did for the first stage instead if we wanted to find the speed at eight seconds we'd have to draw a tangent to the curve at that point because remember a tangent is just a straight line that has exactly the same gradient as the curve does at the point where they touch and to find the speed we need to know the gradient once we have this tangent we can calculate this gradient by picking two points along the line like these two and dividing the change in distance which is around 12 meters by the change in time which is 3 seconds so we get a speed of 4 meters per second so to sum up this video on a distance time graph straight lines represent constant speeds flat lines mean stationary and curved lines represent changing speeds and if you want to calculate the speed at any particular point you need to calculate the gradient of the curve at that point so if the point lies on a straight line like this one then you just calculate the gradient of the line by dividing the change in distance by the change in time if the point lies on a curve though like this one does you need to draw a tangent to the curve at that point and then calculate the gradient of that tangent anyway that's everything for this video so if you enjoyed it then do give us a like and subscribe and we'll see you next time