Thread: Distance Problem :(

The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period in km.

Can anyone help? I'm have no clue what I have to do.

Originally Posted by mathman66

The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period in km.

Can anyone help? I'm have no clue what I have to do.

Well, since there is no attached graph, I can't really help, but I can assume that the graph can be broken down into simpler shapes, which you should find the area of individually and add together to find distance. The area under a velocity-time graph is distance.

Try breaking it into squares, rectangles and triangles, OR, if they give you the equation and you know calculus (I'm assuming you do since this is in the calculus forum), take the definite integral from 0 to 30 (seconds) v(t)dt and that's your distance.

I assume they do not give you the equation shown in the graph? If they did, use the definite integral from 0 to 30. If not, you'll probably only be able to estimate it using Riemann sums. And use midpoints, not upper sums like I did.

Also, note that the Y axis is km/h and the X axis is seconds, so you'll need to convert one of them so the time units match.

Example of estimating with Riemann sums using 3 subintervals (you'll probably want to use more for a more accurate answer):

deltaX = range/subintervals
your range is 30 seconds or 1/2 of 1/60 of an hour or 1/120 of an hour
your deltaX is therefore 1/360 of an hour.

area ~= (1/360)*(value at 1/360 + value at 1/180 + value at 1/120)
area ~= (1/360)*(value at 10 secs + value at 20 secs + value at 30secs)
area ~= (1/360)*(80 + 110 + 120)
area ~= (1/360)*(310)
area ~= 0.861 km

I did that really quickly and probably made a dumb error, so make sure all of that makes sense before you put it all down...