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June 1st, 2009, 12:10 AM  #1 
Newbie Joined: Mar 2009 Posts: 20 Thanks: 0  Using the definite integral to find motion
Hi, The question I've been asked to do is to find s(4) of an object moving in a straight line, given a(t) = , s(0) = 2, v(0) = 3. Am I supposed to use a(t) to solve the equation? All the examples I've seen is just plugging numbers into the equation . Assuming I don't have to use a(t), my working is , giving 85.4. Is this correct? 
June 1st, 2009, 02:55 AM  #2 
Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0  Re: Using the definite integral to find motion
To solve the problem, we must remember that and therefore that In our case, the object has an acceleration function different from that of an object tossed in the air. Integrating twice, we obtain All that remains is to find the values of and and evaluate . 
June 1st, 2009, 12:50 PM  #3 
Newbie Joined: Mar 2009 Posts: 20 Thanks: 0  Re: Using the definite integral to find motion
Thanks for the reply. Another question, for numerical integration, for between 2 and 5, I've drawn a table of values for the f(x) of each (with h = 0.5). Some of these values are negative; would I take the absolute values of these? i.e. my table looks like this x  f(x) 2  0.90... 2.5  0.59... 3  0.14.... 3.5  0.35... 4  0.76.... 4.5  0.97.... 5  0.95... so should I take the absolute value of f(x) 3.5 to 5? 
June 1st, 2009, 01:36 PM  #4 
Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0  Re: Using the definite integral to find motion
In calculating definite integrals, no. Area below the axis is counted as negative area.


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