so in this video we're going to look at how to find distance traveled from a velocity or speed time graph now people often remember the equation that distance traveled equals speed times time now the problem is that we can't use this equation directly if we are in a section like this where the speed is changing so instead we have to use the idea of the area under the curve to find or the line to find the distance traveled so the distance traveled is given by the area under the velocity or speed time graph so if we consider this first for seconds then we need to find the area of this and since it's a triangle we would need to do 1/2 base times height which would give us 1/2 times 4 as the base is 4 times the height of 10 and which would give us 1/2 times 4 times 10 which would give us 20 meters traveled if we had incorrectly just done the final speed times the final time that would employ 40 meters have been traveled and we can sort of understand why that would be wrong because it's only traveling at 10 meters per second right at the end so it must have traveled less distance than 40 meters and the distances traveled works out as 20 if we wanted to work out the distance traveled in the next 4 seconds then we'd be trying to find the area of this rectangle here so the distance traveled in that in the between four and eight seconds would be because that's a rectangle we would just do one side multiplied by the other which would be this side which if you know to get from four to eight so it's four long so we'll do four times the height which is 10 which would give us 4 times 10 which would give us 40 meters and so total distance traveled in those first eight seconds would be 20 plus 40 which would give you 60 meters