Question

question 11 (4 points)
(01.08 hc)
during an experiment, the time of an object was measured every 20 meters. each researcher measured the objects motion on different surfaces, noted as a, b, c, and d. their average data of the trials are shown below.

distance (cm)	0	20	40	60	80	100
time b (s)	0	4.66	9.33	13.97	18.63	23.31
time c (s)	0	3.57	7.44	11.32	16.98	23.28
time d (s)	0	5.00	15.00	40.00	60.00	85.00

which of the surfaces allowed the object to travel closest to a constant speed?
a surface a
b surface b
c surface c
d surface d

Explanation:

Step1: Recall speed - distance - time formula

Speed $v=\frac{d}{t}$, for constant speed, the ratio $\frac{\Delta d}{\Delta t}$ should be constant for equal - distance intervals. Here, $\Delta d = 20$ cm for each interval.

Step2: Calculate speed intervals for Surface A

For Surface A:

• From $d = 0$ to $d = 20$ cm, $v_1=\frac{20}{5.23}\approx3.82$ cm/s
• From $d = 20$ to $d = 40$ cm, $v_2=\frac{20}{10.11 - 5.23}=\frac{20}{4.88}\approx4.09$ cm/s
• From $d = 40$ to $d = 60$ cm, $v_3=\frac{20}{14.68 - 10.11}=\frac{20}{4.57}\approx4.38$ cm/s
• From $d = 60$ to $d = 80$ cm, $v_4=\frac{20}{18.54 - 14.68}=\frac{20}{3.86}\approx5.18$ cm/s
• From $d = 80$ to $d = 100$ cm, $v_5=\frac{20}{23.36 - 18.54}=\frac{20}{4.82}\approx4.15$ cm/s

Step3: Calculate speed intervals for Surface B

For Surface B:

• From $d = 0$ to $d = 20$ cm, $v_1=\frac{20}{4.66}\approx4.29$ cm/s
• From $d = 20$ to $d = 40$ cm, $v_2=\frac{20}{9.33 - 4.66}=\frac{20}{4.67}\approx4.28$ cm/s
• From $d = 40$ to $d = 60$ cm, $v_3=\frac{20}{13.97 - 9.33}=\frac{20}{4.64}\approx4.31$ cm/s
• From $d = 60$ to $d = 80$ cm, $v_4=\frac{20}{18.63 - 13.97}=\frac{20}{4.66}\approx4.29$ cm/s
• From $d = 80$ to $d = 100$ cm, $v_5=\frac{20}{23.31 - 18.63}=\frac{20}{4.68}\approx4.27$ cm/s

Step4: Calculate speed intervals for Surface C

For Surface C:

• From $d = 0$ to $d = 20$ cm, $v_1=\frac{20}{3.57}\approx5.60$ cm/s
• From $d = 20$ to $d = 40$ cm, $v_2=\frac{20}{7.44 - 3.57}=\frac{20}{3.87}\approx5.17$ cm/s
• From $d = 40$ to $d = 60$ cm, $v_3=\frac{20}{11.32 - 7.44}=\frac{20}{3.88}\approx5.15$ cm/s
• From $d = 60$ to $d = 80$ cm, $v_4=\frac{20}{16.98 - 11.32}=\frac{20}{5.66}\approx3.53$ cm/s
• From $d = 80$ to $d = 100$ cm, $v_5=\frac{20}{23.28 - 16.98}=\frac{20}{6.3}\approx3.17$ cm/s

Step5: Calculate speed intervals for Surface D

For Surface D:

• From $d = 0$ to $d = 20$ cm, $v_1=\frac{20}{5.00}=4.00$ cm/s
• From $d = 20$ to $d = 40$ cm, $v_2=\frac{20}{15.00 - 5.00}=\frac{20}{10}=2.00$ cm/s
• From $d = 40$ to $d = 60$ cm, $v_3=\frac{20}{40.00 - 15.00}=\frac{20}{25}=0.80$ cm/s
• From $d = 60$ to $d = 80$ cm, $v_4=\frac{20}{60.00 - 40.00}=1.00$ cm/s
• From $d = 80$ to $d = 100$ cm, $v_5=\frac{20}{85.00 - 60.00}=\frac{20}{25}=0.80$ cm/s

Step6: Compare the consistency of speeds

The speeds for Surface B have the least variation among the different intervals.

Answer:

B. Surface B