<p>A particle moves along the x-axis so that its velocity at any time t≥0 is given by v(t)=(5te^-t)-1. At t=0, the particle is at position x=1. What is the total distance traveled by the particle from t=0 to t=4?</p>
<p>a. 0.366
b. 0.542
c. 1.542
d. 1.821
e. 2.821</p>
<p>The answer is d. 1.821, but I don't understand how. I do know to do the integral from 0 to 4 of the absolute value of v(t), and that comes out as 1.821, but what about the information about "at t=0, the particle is at position x=1" ? Is that part unnecessary information thrown in just to confuse people? I don't understand at all. Please explain!</p>
<p>It’s irrelevant. That information is important only if you were finding the x coordinate of a certain point or trying to find the equation for the position.</p>
<p>Total distance traveled is simply just integrating the absolute value of the velocity over the time interval or integrating the speed</p>
<p>I wouldn’t call that information unnecessary. It’ll probably be used in another part of the question.</p>
<p>No it won’t. It’s a multiple choice question.</p>
<p>After asking my son, the information is definitely irrelevant, but not necessarily thrown in just to confuse you. Like a previous poster mentioned, it could be there for the next question based on the same data. Hope this helps some.</p>
<p>In practice tests I’ve taken there have been times when a multiple choice question referred me back to the previous question.</p>
<p>you have to add the initial value to the integral value. so it would be 1+ ∫abs(v(t)),x,0,4).
the particle starts to move at x=1, the particle may move back and forth but it doesn’t matter because of abs. value. So you have to add the initial value. No, they are there to use it, not to trick you. Hope it helped.</p>
<p>^No, what you said would be correct if the question asked for displacement or the position of the particle and if so the absolute value function shouldn’t be used. But the question asked for distance which does not take displacement into account, so the initial value is not added. </p>
<p>1.821 is indeed the correct answer.</p>
<p>K</p>
<p>Sent from my YP-G70 using CC</p>
<p>d. 1.821</p>
<p>This is so easy, one of my dum friend managed to get a 108% in this class.</p>
<p>Yes, Jimmy, we know that the answer’s D. You should try reading previous replies before you post.</p>