I'm having difficulty with this last homework problem for Physics. I believe I just need to take the integral of the acceleration equation to get velocity. However it's been a number of years since I've taken calculus and I'm in the process of relearning it but I haven't gotten back to integrals yet. Here's the problem-

The acceleration of a motorcycle is given by a(t) = At − Bt^2, where A = 1.50 m/s^3 and B = 0.120 m/s^4. The motorcycle is at rest at the origin at time t=0.

Find velocity as a function of time.


I'm not too terribly concerned with getting the actual answer as I've done all the other problems. I'm mostly looking for some help on integrals in general and if anybody knows any good free online math sites. I've been doing KhanAcadamy to refresh myself but I'm wondering if anybody knows any other good sites for math (especially calculus) information.

this site has a lot of problems you can work, and has step by step solutions if you get stuck
https://www.math.ucdavis.edu/~kouba/ProblemsList.html

but for your problem, maybe this will jog your memory a little:


C is the initial condition, or in this case the initial velocity, which you were told is 0, so C= 0
(the blue squares don't mean anything)

Thanks for the help, im starting to remember this stuff now. That link should be useful I'm finding lots of instructional videos but its nice to have some problems to actually work on. Also, whats the website/program you used to generate that nice image?


One more question. So I found the equation for velocity --- v(t) = .75*t^2−.04*t^3 now it asks to find the maximum velocity attained.

I solved the problem by solving the a(t) equation for zero, when velocity starts to decrease. Then plugged the (t) value back into the velocity equation. Is that the best/only way to solve for this or can you figure this out directly from the velocity equation?

the name of the program is LaTex. You can download and install it, or if you want to do small projects (like what I linked) you can use some online sites. Here is one:
http://arachnoid.com/latex/

I don't have the code anymore I used, but the code for the first line is:





the function decreases from (-infinity , 0) so it has no clear maximum

However, I'm sure what you are really being asked is what is its maximum values when x > 0.

The easy way to find it is take the function and set it equal to 0, then solve for x. Then you must test each solution and the end points of the function to see if they are maximum or minimum (or something else). In this case the interesting solution (your answer) 18.75 (velocity units, can't remember what they were)

ok i'm tried, and I don't have ability to edit my posts, you need to take the derivative of the function and set it equal to 0, then solve for t. Test those solutions and the end points to see if they are a local maximum. And you already have the derivative.

awesome thats what I thought, thanks for the help.