<p>The question is "At what instant does the particle, which moves along a line in such a way that at time t, 1 is less than "t" which is less than 8, reach its maximum speed?</p>
<p>I know that I have to set the absolute value of the velocity equal to 0.</p>
<p>I used the solve key and got weird answers of 5.204, 51.893, and 67.6.</p>
<p>The correct answer is supposed to be 5.896, which I got when I graphed the equation.</p>
<p>Why doesn't the Solve key work for this?</p>
<p>(i'm using the TI89 by the way)</p>
<p>THanks for your help!!!!!</p>
<p>Can somebody plz help me?</p>
<p>thanks in advance!</p>
<p>The particle reaches its maximum speed… when its speed is zero??</p>
<p>Take v(t) and find it’s maximum and minimum over the interval [1,8]. Check v(1), v(8) and all the critical points in between. The velocity with the highest absolute value is the answer.</p>
<p>i jus don’t get why i can’t use the solve key and set the absolute value of the velocity equal to zero, to find the critical points. The highest number that the calculator is supposed to give me would be the maximum.</p>
<p>When I graph it though, i get the right answer…</p>
<p>i just don’t get why the Solve key isn’t working for this. Is it because I can’t utilize the absolute value when using the solve key?</p>
<p>No, if you set velocity to zero, then it’s not moving at all. If you want to find the maximum/minimum of velocity, you need to take the derivative of velocity and set that to zero. What you’re going gives you the points when the particle stops moving and turns around.</p>
<p>If they gave you the position of the object, then you have to differentiate twice, not once.</p>
<p>I’ve had to use the ti-89 for a bunch of problems like these, and it usually does it without complaint. I don’t think having absolute value in there should mess it up.</p>
<p>wait…are you sure about that?</p>
<p>i’ve always been taught that in order to find the maximum/minimum, you need to use velocity, not the derivative of velocity which woudl be acceleration…</p>
<p>Well, if you want to find the maximum of how far the object goes along the line, then you look at velocity, which is the derivative of position. But if you want to find the max/min of how fast the object is going, you need acceleration.</p>
<p>Think about it: if acceleration is positive, then negative, and 0 in between, that means that the object was speeding up until a maximum, and then starts to slow down, with max velocity when a=0.</p>
<p>i’m still not getting the right answer of 5.896 by using the solve key.</p>
<p>I’m really sorry but do you think u can try to use the TI89 to find at what instant the particles reaches the max speed please? and let me know if you got it?</p>
<p>thanks for ur help! :)</p>
<p>Sure! What’s the given equation?</p>