Hi,
See attached. Here's what I understand so far:
A) I understand a, except... well see b..
B) The answer states that it is [0,2.5). How can the instantaneous velocity be positive at t=0 if 0 is not positive or negative. The question states that the particle starts at rest so at t=0 there is no velocity, and thus is not positive.
C) Answer says 6m; if you look at graph, it goes slightly higher than 6; i put 6.5.
D) I understand this question.
E) Here it gets wishy-washy. So the answer is 3, apparently, but since the equation of the parabola is not known, I can't take the derivative and are stuck how they inferred this.
Any help is gladly appreciated.
Okay I am going to give you two ways to approach this problem
So first of all you have the following conditions:
s(0)=0
s(5)=0
s’(2.5)=0
So you can make this differential equation
Integrating both sides will give you this:
Now we know that s’(2.5)=0, so we can plug that in:
So we have:
We can integrate both sides of the differential equation again to get this:
So since we know that c is -2.5a we can make a system of equations.
However this is a very much complicated method of doing it, defintely go with Evolios method, I'm only saying this assuming it's not an exam. However if this was an exam I wouldn't think about building a differential equation. Also (b) is (0, 2.5) since it starts at rest as you said, (c) is anything at least 6 is reasonable. Just eyeball it! It's reasonable to guess anything between 2 and 4. I'd pick 3 because it looks very 3ish to me. If you really wanted to get a precise answer, you'd guess that it's a graph of the form ax(x-5), guess a, then take derivatives. I think guessing a=-1 turns out to be nice so you have f'(1)=3. You can do differential equations if you want but you wouldn't bring a bulldozer to knock down a lego house If your end goal is to do well on an exam, setting up and solving a differential equation would waste at least 5 minutes vs just saying, "looks like 3".