t(s), d (cm), d (cm)
0, 12, 2
5, 15, 2
10, 20, 4
15, 25, 6
20, 29, 8
a) (10 points) One way to find the speed v from
the tabulated data is to calculate
v = ?d/?t
for each pair of successive times and then average
all ve values of v
(hint: the time intervals between successive points are all thesame). Show that this procedure gives
v = (d5 - d1)=(t5 - t1);
which means this method ignores the middle three measurements.Prove this without putting in numbers
(5 points); then nd a numerical answer (5 points). Make sure toshow all intermediate calculations.
b) (15 points) A better procedure is to make a least squares t tothe equation:
d = d0 + vt:
Using the formulas from the lectures notes, and working out thenumbers yourself,
make (by hand) an errorbar plot of d vs t, with t on the x-axis (3points)
calculate the slope (3 points) and its uncertainty (3 points)
calculate the intercept (3 points) and its uncertainty (3points)
You must do this by hand. Show all the required work. If you onlystate the results, you will receive
zero points even if they are correct. You can use MATLAB to checkyour calculations, but you do not
need to include it. However, remember to attach a print out of yourplot to your homework.
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Having so much trouble with this.. It seems simple.. but I amhaving a nightmare figuring where to start.