class 050914

Write down the 4 equations of uniformly accelerated motion.  Time limit:  2 minutes.

Write down the definition of velocity and the definition of acceleration.  Time limit: 2 minutes.

Find the slope and area beneath the following graph, and give the meaning and the units of the slope and the area

• if the graph represents velocity of an object in meters / second vs. clock time in seconds and
• if the graph represents the force exerted on an object in Newtons vs. the position of the object in meters

Solve the equation vf = v0 + a `dt for `dt.  Show your steps.

If you know v0, a and `ds, which of the four equations of uniformly accelerated motion will allow you to solve for vf?

int(f(x),x,0,6)

F = 6.2 x + 3.2 indicates that the best-fit straight-line graph has slope 6.2 andb vertical intercept 3.2.

The meaning of the slope is rise / run = change in force / change in position, and units of the slope are N / ft.

The meaning of an area under the graph is average force * change in position, in units of N * ft.  This is work, in N * ft.

How much work was done in stretching the cord out to an additional length of 6 ft?

I don't really have anything that I need help with right at this moment. I think that everything is going ok for now, but if I have any questions I will know how to send them to you.

<h3>Part of the reason for the assignment is to engage skills related to the process of thinking of and phrasing a good question. Everyone needs to do this.</h3>

I do not understand how to do rapid estimating. Please tell me how to do the following questions. Estimate the order of magnitude (power of ten) of: a)2800 B)86.30 * 10(raised to 2) c) .0076 and D)15.0 * 10 (raised to 8).

<h3>I'll leave it to you to calculate the results for these numbers, but here are some examples:

When rounding to the nearest 10:

Numbers from 1 to 5 round off to 1.
Numbers from 5 to 10 round off to 10.

The order-of-magnitude estimate is obtained by expressing the number in scientific notation, and rounding the first factor to the nearest 10.

So, for example, rounding to the nearest 10:

3.5 rounds off to 1
8.2 rounds off to 10
4.789 rounds off to 1
6.025 rounds off to 10

We use this idea to round off each of the following:

75,000 = 7.5 * 10^4. Rounding the first factor 7.5 to the nearest 10 we get 10, so our order-of-magnitude estimate becomes 10 * 10^4, which is 10^5.

1259 = 1.259 * 10^3. Rounding the first factor 1.259 to the nearest 10 we get 1, so our order-of-magnitude estimate becomes 10 * 10^3, which is 10^4.

.0093 = 9.3 * 10^-4. Rounding the first factor 9.3 to the nearest 10 we get 10, so our order-of-magnitude estimate becomes 10 * 10^-4, which is 10^-3.

How do we find the area inside of a graph?

<h3>You find the area under a trapezoidal region by multiplying average 'altitude' by width. See also notes from 9/9/05.</h3>