#$&*
course PHY121
I struggled with the 2nd half of this question, as noted in the document.3.9.11 at 11:11am
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 # 1, and solve it using direct reasoning.
Accompany your solution with an explanation of the meaning of each step and with a flow
diagram.
Then solve the same problem using the equations of uniformly accelerated motion.
Make up a problem for situation # 8, and solve it using the equations of uniformly
accelerated motion.
#1
Known:
v0=10m/s
vf=30m/s
a=4m/s^2
Unknown:
'dt>>Knowing that the object accelerates at 4m/s^2, it's fairly obvious that it would take 5
seconds to get from a velcoity of 10m/s to 30m/s.
'ds>>After the 5 second interval the change in position would be 100m. The average velocity
is 20m/s. Multiplying that by the 5 second interval would result in the change in position.
#8
Known:
vf=30m/s
a=4m/s^2
'ds=100m
Unknown:
v0
'dt
a_Ave=(vf-v0)/'dt
vAve=(v0+vf)/2
'dt='ds/vAve
'ds=(v0+vf)/2*'dt
I cannot think of a way to solve it by just using waht is 'known' here. It doesn't seem to
fit any of the equations? What am I missing or not seeing here?
"
@& You need to know the equations of uniformly accelerated motion, which you should have encountered a number of times at this point in the course.
I listed them for you in previous posting.*@