course phy 121
2/10 at 2:12 p.m.
Solving Uniform Acceleration Problems--------------------------------------------------------------------------------
Possible Combinations of Variables Direct Reasoning
Using Equations Problem
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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 # 10, 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.
Problem # 10 - If we know that a=.5 m/s and dt= 20 s and ds=400 meters, solve for v0 and vf.
'ds=v0'dt+.5a'dt^2
400 m = v0(20s)+.5(.5m/s^2)(20s)^2
400 m =v0(20s) + 100m
300 m =v0(20s)
15 m/s= v0
vf= v0 +a* 'dt
vf= 15m/s + .5m/s^2(20s)
vf= 15m/s + 10 m/s
vf= 25 m/s
Good solution.
Problem #8 - If vf= 20 m/s and dt = 30 s and ds= 300 meters, solve for a and v0.
This doesn't fit the given information for situation #8, in which you know only vf, a and `ds.
You have assumed the values of vf, `dt and `ds, not vf, a and `ds.
'ds=(v0+vf)/2 * 'dt
300 m = (v0 + 20 m/s)/2 * 30 s
10 m/s = (v0 + 20 m/s)/2
20 m/s = v0 + 20 m/s
0 m/s = v0
vf= v0 + a* 'dt
20 m/s = 0m/s + a(30 s)
.667 m/s^2 = a
As on the preceding submission, you have a very good solution of the first situation, but didn't use the correct information to find the second.
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