# How to work out distance from a velocity-time graph when line is curved?

1. Jun 4, 2010

### manu442

Question from a mock exam I was looking over:
1. The problem statement, all variables and given/known data

I have a velocity-time graph and I understand the distance is the area underneath it, but the line is curved, so how can I calculate the area under it?
If possible show how you calculated distance under A,B,C,D (MOSTLY B AND C)
Thanks

Image: http://tinypic.com/r/2zohgd0/6

3. The attempt at a solution

The question in the exam was to find distance is section C and this is what I did (I had no clue, just guessed):

S=D/T
2=D/10
D=2*10
=20m travelled

Last edited: Jun 4, 2010
2. Jun 4, 2010

### RoyalCat

If you know the formula of the curve, then you can simply integrate (The area under the graph of a function, stretching between two points, A and B, is the definite integral of that function evaluated between A and B)

If you do not, then you can approximate it numerically. Cut the area into sufficiently small triangular or trapezoid pieces (You know how to calculate those areas), and the smaller your dicing is, the better an approximation will your calculation be to the actual area under the graph. (This is literally doing an integral by hand, without the formula for the function)

3. Jun 4, 2010

### manu442

hmm ok thanks, I doubt we'll get formulas in the test, but I'll try the method of chopping down the curve