Time and Date Stamps (logged): 17:12:20 06-10-2020 °¶Ÿ°±Ÿ±¯¯µŸ°¯Ÿ±¯±¯ Calculus I

Physics I Major Quiz

Completely document your work and your reasoning.

You will be graded on your documentation, your reasoning, and the correctness of your conclusions.

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Instructions:

Directions for Student:

Test Problems:

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Problem Number 1

Give an example of a situation in which you are given a, Ds and Dt, and reason out all possible conclusions that could be drawn from these three quantities, assuming uniform acceleration. Accompany your explanation with graphs and flow diagrams. Show how to generalize your result to obtain the symbolic expressions for v0 and vf.

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Problem Number 2

A straight ramp is inclined at three different slopes. The differences in elevation between one end and the other, for the different slopes, are 2.1, 4.2 and 5.8 cm.

How well do these data confirm our suspicion that the acceleration on the ramp is linearly dependent on the slope?

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Problem Number 3

Solving Uniform Acceleration Problems

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. 

Problem

Do the following: 

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Problem Number 4

A projectile leaves the edge of a table and falls freely a distance of 150 cm to the floor. It travels a horizontal distance of 6.1 cm during its fall. How long does it take to fall and what is its horizontal velocity during the fall?

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Problem Number 5

If the velocity of the object changes from 5 cm / sec to 16 cm / sec in 5 seconds, then at what average rate is the velocity changing?

A cart rolling from rest down a constant incline of length 64 cm requires 8.8 seconds to travel length of the incline.

An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.

At what average rate does the velocity of an automobile change, if it accelerates uniformly down a track, starting from rest, and if it requires 14 seconds to cover a distance of 169 meters.