course phy 201
Solving Uniform Acceleration Problems--------------------------------------------------------------------------------
Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.
Possible Combinations of Variables Direct Reasoning
Using Equations Problem
--------------------------------------------------------------------------------
Possible Combinations of Variables
There are ten possible combinations of three of the the five variables v0, vf, a, Dt and Ds. These ten combinations are summarized in the table below:
1
v0
vf
a
2
v0
vf
dt
3
v0
vf
ds
4
v0
a
dt
5
v0
a
ds
*
6
v0
dt
ds
7
vf
a
dt
8
vf
a
ds
*
9
vf
dt
ds
10
a
dt
ds
If we know the three variables we can easily solve for the other two, using either direct reasoning or the equations of uniformly accelerated motion (the definitions of average velocity and acceleration, and the two equations derived from these by eliminating Dt and then eliminating vf).
Only two of these situations require equations for their solution; the rest can be solved by direct reasoning using the seven quantities v0, vf, a, Dt, Ds, Dv and vAve. These two situations, numbers 5 and 8 on the table, are indicated by the asterisks in the last column.
Direct Reasoning
We learn more physics by reasoning directly than by using equations. In direct reasoning we think about the meaning of each calculation and visualize each calculation.
When reasoning directly using v0, vf, `dv, vAve, `ds, `dt and a we use two known variables at a time to determine the value of an unknown variable, which then becomes known. Each step should be accompanied by visualization of the meaning of the calculation and by thinking of the meaning of the calculation. A 'flow diagram' is helpful here.
Using Equations
When using equations, we need to find the equation that contains the three known variables.
We solve that equation for the remaining, unknown, variable in that equation.
We obtain the value of the unknown variable by plugging in the values of the three known variables and simplifying.
At this point we know the values of four of the five variables.
Then any equation containing the fifth variable can be solved for this variable, and the values of the remaining variables plugged in to obtain the value of this final variable.
Problem
Do the following:
Make up a problem for situation # 4, and solve it using direct reasoning.
vo,a,'dt
aAve=(vf-vo)/'dt
average acceleration is determined by teh change in velocity divided by the change in time.
Accompany your solution with an explanation of the meaning of each step and with a flow diagram.
first subtract the initial velocity from the final velocity and then divide that answer by the change in time.
'dt 'ds vo
! \ / / /
! vAve / /
! \ / /
! vf -- / /
! \ /
a------'dv
Then solve the same problem using the equations of uniformly accelerated motion.
vf=vo+a'dt
Make up a problem for situation # 5, and solve it using the equations of uniformly accelerated motion.
vo,a,'ds
'ds=vo'dt+.5a'dt^2
By 'make up a problem' the question means that you should assign values to the given quantities and work out the solution for two remaining quantities.
It seems clear that you could have done this; if you are at all uncertain of your ability to do so you should resubmit. If you are confident, then you need not do so.