## 24-Hour Contest Begins NOW

We hit 100 likes on Facebook, so it’s time for a 24-hour contest that tests your creativity. The prize is a signed copy of Mike’s new book, so head over to our Facebook page and post your response now!

Thanks for being a part of the Calculus-Help.com relaunch. Every 100 likes we get on Facebook sparks a new contest, until I run out of prizes. Each contest will only run for 24 hours, so keep your eyes peeled and let your creative flag fly!

## Big Announcement #1 (of 2)

Big news. Huge. Enormous. Large, even. A major part of Calculus-help is about to return.

The Problem of the Week is back! Each Saturday morning you can click on the “Problems” link in the site menu to see a brand-spanking-new Problem of the Week with a full solution. What can you do with a Problem of the Week? Use it to review the topics you’re covering in class, or come back later and work through them to prepare for quizzes and tests. (After all, the answers are included.)

Two problems are currently posted, and the third will appear, as if by magic, by September 17. Each Saturday, until the end of the academic year, a new Problem will be posted.

Let me know what you think. This is a new era for Calculus-Help.com, but this is only phase one. Stay tuned for another Big Announcement soon.

## Mike’s New Book Is Full of Math, Fun, and (Hopefully Not) A Human Tooth!

Remember how excited Dorothy was when she landed in Oz? She was in a new place, filled with color and tiny people who could sing and dance perfectly choreographed routines without even rehearsing! Even better, she had a mission. Simply follow the yellow brick road and everything would be wonderful. This is powerful magic indeed. Remember, all of this frolicking is going on not twenty feet from a recently-crushed witch corpse, but no one seems to mind.

Do you feel like Dorothy, ready to step out onto the long, magical road of math, full of excitment, dread, and also pigtails and/or a tiny dog? Are you someone lost along the way to Oz and starting to wonder whether it was really worth stopping to help that scarecrow down? I mean, he can’t even add fractions for the love of corn. The Humongous Book of Basic Math and Pre-Algebra Problems will take you through the poppy fields, away from the flying monkeys, and right up to the front door of Oz, all oiled up and ready to go.

Feel like you need a new brain when you’re in a math class? Are your computational skills all rusty, Tin Man? Maybe a big boost of courage is all you really need to be toto-ly prepared. If you are about to take an algebra class (or have a friend that desperately needs your help), don’t wait! Click this link to BUY TODAY!

Want to learn more about Mike’s other books? (Spolier alert: Yes, you do.) Click here!

## Calculus-Help now 26.2% more fun!

By popular demand, this week’s slate of updates heralds the return of music to Calculus-Help.com. Now available on the main links bar at the top of every page, you’ll find a link to “Fun.” Follow this link to listen to, or download, the (oddly) ever popular Quadratic Formula song. You may also want to settle down to the soothing lyrics of The Day Before Notebooks Are Due Blues or The A.P. Calculus Theme Song. It’s not even close to the holiday season, but does that mean you can’t go and enjoy some holiday carols involving Calculus? (Hint: no.)

If mathematical music is not your thing, that’s okay–it’s not most people’s thing either. The new page o’ fun also ushers in the return of the Interactive Cheat Sheet, a flash-based application that presents the most important calculus formulas in one location.

In honor of music’s return to Calculus-Help.com, keep your eyes fixed on this very page, because a contest is looming. Perhaps you have a calculus song burning in your very soul. You just may get the chance to unburden said soul for prizes!

## Problem 15: A Grizzly Motion Problem

2011-2012

The motion of a grizzly bear stalking its prey, walking left and right of a fixed point in feet per second, can be modeled by the motion of a particle moving left and right along the x-axis, according to the following acceleration equation:

Assume that the origin corresponds to the fixed point, and that a positive value for position means that the bear is located to the right of the fixed point as we watch said bear from a safe location.

If the bear’s velocity is 1 ft/sec when t = 0, answer the following questions:

(a) Identify the velocity equation that represents the bear’s motion.

(b) Determine how fast the bear was traveling at t = 7 seconds.

(c) In what direction is the bear traveling at t = 5 seconds?

(d) How far does the bear walk during the first 10 seconds?

Note: You can (and should) use a graphing calculator for part (d).

### Solution:

(a) You are given the acceleration equation. Recall that velocity is the antiderivative of acceleration, so integrate a(t) and use the fact that v(0) = 1  to identify the velocity equation.

(b) Evaluate v(7).

Speed is the absolute value of velocity, so the bear is traveling at a speed of 1.579 ft/sec when t = 7.

(c) Evaluate v(5).

Because v(5) is negative, the bear is traveling left at t = 5.

(d) You must split the interval [0,10] into segments based on the t-intercepts of v(t). Those values of t are the times at which the bear changes direction; you must measure how far the bear traveled forward and backward separately.

The velocity equation has only one t-intercept on [0,10]: t = 1.17012095. To calculate the total distance traveled, compute the area between v(t) and the t-axis on the intervals [0,1.17012095] and [1.17012095,10] independently. When the bear is traveling left, this integral is a negative value, but you are asked to find the total distance traveled, not the final position of the bear. Therefore, both integrals must be positive values, so take the absolute value of the second definite integral.