Need help on FIRST DAY CALC HWMK :O

Pre-College Topics High School Life
1

<p>I’ve been a CC lurker for quite some time, but have only recently decided to make an account. </p>

<p>most because I seem to have lost all of the information I attained (or thought I did) during pre-calc.</p>

<p>I’m a junior in Calc BC, and I need help on our first assignment.</p>

<p>The question…
We were given a graph that shows speed in meters per second on the y-axis and time in seconds on the x-axis. The graph looks a bit like this</p>

<p><a href=“http://www.■■■■■■■■■■/photos/11455275@N03/1121185208/[/url]”>http://www.■■■■■■■■■■/photos/11455275@N03/1121185208/&lt;/a&gt;&lt;/p&gt;

<p>Assignment: Make a graph that shows the acceleration over time. Then, make another graph that shows the distance over time.</p>

<p>Only way I can think of doing it is:

  1. acceleration over time - find the difference between the velocities (previous and current)
  2. distance - multiply the speed and seconds. then, add that distance to whatever distance previous that you’ve traveled so far.</p>

<p>is there a better way to do this? derivatives maybe (i forgot how to find the derivatives of a graph!) my way seems highly unsophisticated and prone to mistakes - and long. plus, my teacher said there were better ways to do it.</p>

<p>thanks for your help</p>

2

<p>The derivative of speed is acceleration, to find it on a velocity/time graph, the acceleration is the slope. The integral of speed is distance, so the area under the curve would be the distance travelled.</p>

3

<p>How can I find the slope and the area under the curve of a graph that looks like the one I mentioned?</p>

<p>Do I make rectangles/triangles to find the area under the curve?</p>

<p>Thanks for the reply, by the way.</p>

4

<p>For slope/area:</p>

<p>It depends. If they give you the equation of the line, you can get the slope from that, and you could also get the area under the curve by integrating it, but you might not know how to do that yet. </p>

<p>If they don’t give you the equation of the line, you can’t give an exact answer for slope or area… so you have to estimate. You could use rectangles or triangles like you suggested… or you could always do a line of best fit, and then it’s just a trapezoid.</p>

5

<p>Oh okay. Thanks! I guess I will do a line of best fit, then, since they did not provide the equation.</p>