course Phy 201
If the velocity of the object changes from 4 cm / sec to 16 cm / sec in 8 seconds, then at what average rate is the velocity changing?vAvg= ‘ds/’dt= vAvg = 16-4/8 = 12/8 = 1.5 cm/sec
A ball rolling from rest down a constant incline requires 8.2 seconds to roll the 97 centimeter length of the incline.
• What is its average velocity?
• vAvg=’ds/’dt = 97cm/8.2sec= 11.83cm/sec
An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.
• What therefore is the final velocity of this ball?
• 11.83*2= 26.66
The numbers are right; what are the units?
• What average rate is the velocity of the ball therefore changing?
• It is twice the amount in which it begins.
The following questions should be asked and answered in order to determine the average rate of change of velocity with respect to clock time on an interval:
What is the initial velocity on this time interval?
What is the final velocity?
How long does the time interval last?
What therefore is the average rate of change of velocity with respect to clock time?
Can you insert your answers to these questions, as indicated below?
An automobile accelerates uniformly down a constant incline, starting from rest. It requires 10 seconds to cover a distance of 132 meters. At what average rate is the velocity of the automobile therefore changing?
vAvg= ‘ds/’dt = 132meters/10sec = 13.2meters/sec
This question gives tells you how far an object moves in a given time interval, accelerating uniformly from rest.
Like most students you calculate the correct average rate of change of position with respect to clock time. This is good.
However the average rate of change of position with respect to clock time is very different from the average rate of change of velocity with respect to clock time, which is what the question asked for. This must be determined using reasoning similar to that outlined in the preceding questions.
random problem 1 assignment 3 c
The following is a solution to the given problem.
Please compare the given solution with your solution and submit a self-critique of
any error(s) in your solutions, and/or and additional questions or comments you
might have.
Simply copy your posted document into a text editor and insert revisions, questions, and/or self-critiques, marking your insertions with ####.
Submit using the Submit Work Form.
The first question, in which you are given v0,
vf and `dt, is easily answered; just divide the change in the
given velocities by the given time interval.
In the 'middle' sequence of questions you are given the following:
- Initial velocity is 0 and acceleration
is uniform on
this interval.
- The displacement `ds is specified.
- The time interval `dt is specified.
You are asked to find the average velocity, final velocity
and average rate of change of velocity with respect to clock time on the
interval.
- The average velocity is vAve = `ds / `dt
, which
follows immediately from the definition of average velocity as average rate
of change of velocity with respect to clock time.
- Since the condition that 'initial velocity is 0
and
acceleration is uniform' applies to motion on this interval, the final
velocity is double the average velocity, as described in the problem.
So the average velocity can be doubled to get the final velocity
Thus we easily reason out the average and
final velocities. We must still calculate the average rate of change
of
velocity with respect to clock time.
The following questions should be asked and
answered in
order to determine the average rate of change of velocity with respect to clock
time on an interval:
- What is the initial velocity on this time interval?
- What is the final velocity?
- How long does the time interval last?
- What therefore is the average rate of change of velocity with respect to
clock time?
All steps should be described in your solution.
- Your reasoning should be outlined.
- If you are calculating an average velocity (i.e., an
average rate of change of position with respect to clock time), or average
acceleration (i.e., an average rate of change of velocity with respect to
clock time), you should verify in your solution that you have correctly
identified the quantities being used and that you have applied the
definitions carefully.
- Units should be included at every step of
every
calculation.
Calculation of `ds / `dt typically involves `ds in cm
or in m, and `dt in seconds, so that `ds / `dt will be in units of cm / s or
m/s.
Calculation of `dv / `dt typically involves `dv in
cm/s and `dt in seconds, so that `dv / `dt is in units of (cm/s) / s =
cm/s^2, or (m/s) / s = m/s^2.
The very last question gives tells you how far
an object
moves in a given time interval, accelerating uniformly from rest.
- Most students calculate the correct average rate of change of position
with respect to clock
time. This is good. However most students stop there, thinking they have answered the question.
- The question did not ask for average rate of
change of position with respect to clock time, but for average rate
of change of velocity with respect to clock time. Calculating
the average rate of change of position is a necessary step in
the process, but it does not give the requested final result.
- The average rate of change of position with respect
to clock time is very different from the average rate of change of velocity
with respect to clock time, which must be determined using reasoning similar
to that outlined in the preceding questions.