Sign up for your FREE 7-day trial.Get instant access to all the benefits of SparkNotes PLUS! Cancel within the first 7 days and you won't be charged. We'll even send you a reminder.
SparkNotes Plus subscription is $4.99/month or $24.99/year as selected above. The free trial period is the first 7 days of your subscription. TO CANCEL YOUR SUBSCRIPTION AND AVOID BEING CHARGED, YOU MUST CANCEL BEFORE THE END OF THE FREE TRIAL PERIOD. You may cancel your subscription on your Subscription and Billing page or contact Customer Support at custserv@bn.com. Your subscription will continue automatically once the free trial period is over. Free trial is available to new customers only.
Step 2 of 4
Choose Your Plan
Step 3 of 4
Add Your Payment Details
Step 4 of 4
Payment Summary
Your Free Trial Starts Now!
For the next 7 days, you'll have access to awesome PLUS stuff like AP English test prep, No Fear Shakespeare translations and audio, a note-taking tool, personalized dashboard, & much more!
Thanks for creating a SparkNotes account! Continue to start your free trial.
Please wait while we process your payment
Your PLUS subscription has expired
We’d love to have you back! Renew your subscription to regain access to all of our exclusive, ad-free study tools.
Problems for Position Functions in One Dimension 1
TopicsProblems for Position Functions in One Dimension 1
Did you know you can highlight text to take a note?x
Problem :
Find the position function for an elephant on a tightrope if the elephant's
path goes as follows: (1) the elephant begins 5 ft to the right of the
origin (center of the tight rope), (2) the elephant moves left at a steady
pace for 3 minutes and ends up 2 ft left of the origin, (3) the elephant
stays still at that spot for 1 minute, and (4) the elephant moves right at a
steady pace for another 2 minutes and ends up 1 foot to the right of the
origin.
Our first task in tackling this problem is to write down everything we
already know about the position function x(t). From (1) we know that
x(0) = 5. (2) tells us that x(3) = - 2, and (3) indicates that x(t) = - 2 for
all t between 3 and 4. Finally, from (4) we know that x(6) = 1.
Because the elephant always moves "at a steady pace," we can plot these
known points on the graph of the position function and fill in the rest by
drawing straight lines between them. The final position function, defined
for t valued between 0 and 6, looks like:
Figure %: The position function for an elephant on a tightrope.
Unlike other position functions we've discussed thus far, this one cannot be
written as a single equation--algebraically it must be defined in pieces.
For this reason it's a little easier to represent the solution graphically.
Problem :
Plot the position function given by x(t) = - gt2 + h for g = 9.8 and
h = 40.