Calculus AB problems help?

Test Preparation AP Mathematics & Computer Science
1

<p>Please help with these problems by showing how you got the answers also.
I especially want to know how to solve #1.</p>

<ol>
<li><p>If a 2-kg object is dropped from rest, its kinetic engergy E (in joules) increases according to the differential equation dE/dt = 192t where t is measured in seconds. If the initial kinetic energy is 0J, what is the kinetic energy after 5 seconds?</p></li>
<li><p>A chain weighs 0.5 pound per foot of length. If a 36-foot length of this chain is hanging from the edge of the roof of a tall building, how much work will it take to pull the chain up onto the roof? (Round to the nearest 25ft-lb)</p></li>
</ol>

2

<p>I think this is how you do it: For number 1, multiply both sides by dt. So you get dE = 192t dt. Then integrate from 0 to 5 to get E. </p>

3

<p>Muahaha, I can solve these in 10 seconds using physics methods!</p>

4

<p>Cheap solution for 2: By symmetry (since the chain’s mass is evenly distributed), the problem is equivalent to computing the work done by moving an 18 lb mass that is 18 ft from the top. (you can also evaluate W = ∫ ΔE ds). The amount of work done is (18 lb)(18 ft) = 324 ft*lb.</p>

<p>Btw, these don’t seem like AP Calculus problems - #2 assumes that you know what work is, which AP Calculus shouldn’t assume.</p>