in the last video we did we looked at distance time graphs which show us how the distance of an object varies over time in today's video though we're going to focus on velocity time graphs which show us how an object's velocity changes over time these graphs both look pretty similar and it's really easy in exam to get the two of them confused so just be really careful and double check which one you're looking at as these graphs have velocity on the y-axis and time on the x-axis if you want to find the gradient of the curve at any point we have to do the change in velocity over the change in time which you might notice is the formula for acceleration so on a velocity time graph the gradient tells you the acceleration this means that if the curve has a constant positive gradient like it does in this first section then it must be experiencing a constant acceleration whereas if the curve has a constant negative gradient like in the last section then there must be constant deceleration we can calculate the acceleration or deceleration by plugging the relevant numbers into our equation for example in this first section the change in velocity is three meters per second and the change in time is two seconds so the acceleration would just be three divided by 2 so 1.5 meters per second squared now flat sections of the curve have a gradient of 0 and so aren't accelerating at all which means that their velocity is constant because it's not increasing or decreasing so to find the velocity during these stages all we have to do is look at the y-axis so in this second stage the velocity would be three meters per second and in this fourth stage it would be five meters per second if the curve gets steeper like in this third stage the gradient must be increasing and so this means that the rate of acceleration is increasing as well the last thing we need to look at is how to find the distance that was traveled for this we need to find the area under the curve so if we wanted to find the distance traveled in the first four seconds we'd be interested in this area and to make it easier to calculate we could split the area up into a triangle on the left and a rectangle the formula for the area of a triangle is one-half base times height so in this case that would be 0.5 times 2 which is our time times 3 which is the velocity so together that gives us 3 meters then to calculate the area of the rectangle we have to do base times height so just two times three which is six meters so the total area and that's the total distance traveled during these first four seconds would be three plus six so nine meters one of the odd things to be aware of here is that even though area is usually given in meters squared because we're finding the distance traveled we just leave the answer in meters it's just one of those odd things you have to accept now calculating the area under curved parts of the graph is a bit trickier and if you only have to estimator then you'll be given a grid as the graph background like this and you can find the area by counting the number of squares under that section of graph for example in this graph each square in the grid is equal to one meter of distance traveled so for our curved section we've got six full squares one square that's nearly filled and these other two that are almost heartful for these partially full ones you want to try and combine them to make a full square so here we can count these two halves as one whole and then if we add up all of our blue squares together we put a total of almost eight squares which means that the total distance traveled over these two seconds would be around eight meters anyway that's everything for this video so if you enjoyed it then please do tell your friends and your teachers about us and we'll see you next time