B. A particle can travel very quickly over a long distance. Scientists also use a particle accelerator to see how fast a particle can travel. If a particle is put in a particle accelerator, what is the distance traveled over the full 49 minutes?
C. Table 1.1
|
t (minutes)
|
0
|
3
|
6
|
10
|
13
|
17
|
|
Y = m(t)
(distance in cm)
|
0
|
72
|
92
|
144
|
180
|
216
|
D. (See graph below)
E. 180-92/13-6 = 88/7 = 12.57
144-72/10-3 = 72/7 = 10.29
216-144/17-10 = 72/7 = 10.29
At x = 10, points are (10, 12.57), (10, 10.29), and (10, 10.29)
F. The Average Rate of Change (ARC) of the secant lines increase as the other points get closer to 12.18
G. 144-94/10-6 = 50/4 = 12.5. This means that the from minute 6 to minute 10 that the particle traveled 12.5 cm to the next point, a sharper increase than before.
H. I know that the point traveled 12.18 cm before, and therefore the line follows that point. This is only an approximation however, it is not completely exact, and the point intersects it at (10,144) therefore it follows the linear line and creates a tangent.
E. 180-92/13-6 = 88/7 = 12.57
144-72/10-3 = 72/7 = 10.29
216-144/17-10 = 72/7 = 10.29
At x = 10, points are (10, 12.57), (10, 10.29), and (10, 10.29)
F. The Average Rate of Change (ARC) of the secant lines increase as the other points get closer to 12.18
G. 144-94/10-6 = 50/4 = 12.5. This means that the from minute 6 to minute 10 that the particle traveled 12.5 cm to the next point, a sharper increase than before.
H. I know that the point traveled 12.18 cm before, and therefore the line follows that point. This is only an approximation however, it is not completely exact, and the point intersects it at (10,144) therefore it follows the linear line and creates a tangent.
I think you did a great job at justifying your IRC. I think you explained your results well and did well with including your units.
ReplyDeletegriffin,
ReplyDeletei like your topic and your table is well organized and easy to read. i couldn't see the second image that you inserted. i was a little confused by your first secant calculation. the two following are for t = 10 minutes, but the first one is using either t = 6 or 13? i can't really tell. also, there was no need to write the values of your secant lines as ordered pairs, you could have just written the values, 12.57, 10.29, and 10.29 and also remember to write the units of your secant calculations.
your explanation for the tangent line and IRC could have used a little more detail, but it is good. you got a really good tangent line approximation!
other than the calculation confusion, your post is good.
professor little