IbTrojan Posted February 22, 2015 Report Share Posted February 22, 2015 I'm studying for my math test and there's this one question I'm just not getting. A particle moves along a horizontal line with velocity given by v(t) = 2t^2 - 11t +12 where t is greater than or equal to zero. Find the total distance the particle travels from time 2 seconds to time 5 seconds. The question also asks to find acceleration and "a" and "b" if the particle is moving left for a<t<b. Both of which I have figured out. It's just the total distance I can't figure out. We've done other problems in class and I figured them out. My teacher said just to graph it and write out an expression based on the graph and I tried doing that but...I'm getting a really weird negative number Help would very much be appreciated, thank you! Reply Link to post Share on other sites More sharing options...
Vioh Posted February 23, 2015 Report Share Posted February 23, 2015 I'm studying for my math test and there's this one question I'm just not getting. A particle moves along a horizontal line with velocity given by v(t) = 2t^2 - 11t +12 where t is greater than or equal to zero. Find the total distance the particle travels from time 2 seconds to time 5 seconds. The question also asks to find acceleration and "a" and "b" if the particle is moving left for a<t<b. Both of which I have figured out. It's just the total distance I can't figure out. We've done other problems in class and I figured them out. My teacher said just to graph it and write out an expression based on the graph and I tried doing that but...I'm getting a really weird negative number Help would very much be appreciated, thank you! Here is the theory about how to solve for the distance (i.e. areas under the velocity-time graph) that you've probably learned from the textbook: I don't really know whether this is a calculator or a non-cal question, so i'll solve using both Non-Cal (corresponding to Case 2 Method 1 in the theory):Solve the quadratic equation , we'll get or . And since isn't within the range of 2 --> 5, thus we can ignore that solutionSplit the range into two parts; the first range is from 2 --> 4, and the 2nd range is from 4 --> 5According to the theory, we basically have to solve the following 2 definite integral to get the total distance travel, which is: With GDC (corresponding to Case 2 Method 2 in the theory): I'll show the steps using my Ti-84plusGraph the quadratic function . Pay attention to the absolute value sign Using the definite-integral command on your GDC to find the area under the graph from 2 to 5 The final result obtained from the GDC is 7.83 I hope this gave the right answer. Feel free to ask if there's any further questions! 1 Reply Link to post Share on other sites More sharing options...
IbTrojan Posted February 23, 2015 Author Report Share Posted February 23, 2015 (edited) Thank you so much!!! I realize now, looking at the way I solve it that the mistake I was making was SUBTRACTING the two integrals rather than adding them. Thanks again Vioh!! So it's absolute value because it's the distance traveled and that doesn't need a direction, right? Edited February 23, 2015 by IbTrojan Reply Link to post Share on other sites More sharing options...
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