Question

You're testing a wind-up toy car to see if it travels in at a constant speed when let go. You first measure the time t2 it takes to travel across two floor tiles. Then you wind it up and let it roll across four floor tiles, and measure the time t4 for that. The measurements are:

t2 (s) 1.26, 1.25, 1.29, 1.30, 1.21

t4 (s) 2.55, 2.66, 2.50, 2.58, 2.62

(a) Find the average times t2 and t4, rounded appropriately, for each part of the experiment. Verify that the uncertainties for the two sets of measurements are below 5%. Show work.

(b) If the car travels at a constant speed, then t4 ought to be twice as long as t2, since the car traveled twice as far. Calculate the predicted t4 from the average t2. Looking only at the predicted t4 and the measured t4, and ignoring uncertainty, does it appear that the car traveled at constant speed, or that it sped up or slowed down? Explain; write out the values of each quantity referred to.

(c) Now, the average measured t4 has an uncertainty, so we can only assume that the actual time it takes the car to cross four tiles is somewhere within a range defined by the average t4 and its uncertainty. Given that range of uncertainty, does it appear that the car traveled at constant speed, or that it sped up or slowed down? Explain; write out the values of each quantity referred to

Answer 1

a. given data

t2 t4

1.26 2.55

1.25 2.66

1.29 2.5

1.3 2.58

1.21 2.62

Avg 1.262 2.582

a. average t2 = 1.26 s

average t4 = 2.58 s

SD for t2 = 0.035637

SD for t4 = 0.061806

hence

uncertianity in t2 is 3.56%, but in t4 is 6.18%

b. 2*t2avg = 2.524 s

t4 = 2.582 s

compairing these two and ignoring uncertainity, the car seems to have slowed down as time has increased

c. considering uncertainity of t2

2*t2 = 2.524 +- 0.071274

t4 = 2.582 +- 0.06186

as there are overlapping regions inboth ranges where 2*t2 ansd t4 agree , we can agree that the car is travelling at constant speed within limits of unvcertianities