Solution to problem 4 of page 55 in textbook.
First of the Two Questions:
Set up the symbols, there are four important symbol categories::
Given: vi = 15 m/s, a = - 2 m/s/s , vf = 10 m/s
Hidden givens: none in this problem, more common in gravity problems
Solving for: t = ? in the first question
Don’t care: which of the five important symbols (vi, vf, Δx, a, t) do you not care about for THIS question? Think about it. Then simply write that symbol down.
Some comments: writing “t = “ is extremely important, because it tells me which of the four Page 58 equations to look at. Look for one that DOES have t in it. That means I should NOT bother with the fourth equation on Page 58, because it lacks t.
The Don’t Care category is very useful, because it refers to the symbol that I am NOT solving for and also am NOT given. If you visualize the problem, then that Don’t Care quantity is Δx, because refers to a distance, and in the first question, time is asked for.
The rest of this is only easy, because I took the time to write symbols (vi, vf, Δx, a, t) for ALL of the above measurements AND unknowns.
And now I choose the Page 58 formula that LACKS the Don’t Care quantity. And that’s what makes this simple, and because I know on the first quiz I’m only graded on the setup and not the answer, I know I’ll do well, because I’m someone who has the habit of writing the solutions with good notation.
II. Choose the equation that lacks what I don’t care about:
Eqn: ______You write it off of page 58.
III. Show substitutions of the knowns into the chosen equation:
(10 m/s) = ( ) + ( )(t) You fill it in.
IV. Do algebra and get your answer:
YOU do the algebra.
Prove the answer below is true
Ans: after you plugged things into vf = vi + at, algebra told you that t = 2.5 s.
Now do your own setup to solve the “how far” question on the same problem, and don’t look at Page 2 of this document until you have fully tried it on your own.
Second of the Two Questions:
Set up the symbols, there are four important symbol categories::
Given: vi = 15 m/s, a = - 2 m/s/s , vf = 10 m/s
Hidden givens: none in this problem, more common in gravity problems
Solving for: Δx = ? in the second question
Don’t care: Normally would be t, but now since I know t, I have multiple ways to solve this problem.
Some comments: writing “Δx = “ is extremely important, because it tells me which of the four Page 58 equations to look at. Look for one that DOES have Δx in it. That means I should NOT bother with the second equation on Page 58, because it lacks Δx.
The Don’t Care category is very useful, because it refers to the symbol that I am NOT solving for and also am NOT given. If you wanted to, you could interpret this Don’t Care quantity as t, and if you had done that, then your choice of equation to use would have been vf2 – vi2 = 2(Δx)a, because it lacks t. Plugging givens directly into this ugly equation would have yielded a correct answer for Δx.
HOWEVER, since this is a second part of the problem, you already do know t, so things are a little easier. I like to stick to my word which in class was “for now, let’s just focus on the first of the two Page 58 equations.” That means Δx = [(vf + vi)/2]t and vf = vi + at. Since we know all symbols except Δx, let’s plug knowns into Δx = [(vf + vi)/2]t to solve for Δx.
II. Choose the equation:
Eqn: ______You write it off of page 58.
III. Show substitutions of the knowns into the chosen equation:
Δx = [(vf + vi)/2]t = [(( ) + ( ))/2]( ) You fill it in.
= [(10 m/s + 15 m/s)/2](2.5 s) = (12.5 m/s)(2.5 s)
= (12.5)(2.5) = 31.25 (m/s)*s = 31.25 m
That last algebra was one of three ways to use an equation to prove that answer. You prove the other two methods, getting the same final answer.