Find the relationship in a data table and graph

Answer Key - Grade 11 Science Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   A best-fit line of distance fallen d (m) against t² (s²) has slope 4.9 m/s². How long does a ball take to fall 2 m, to 0.01 s, Ari?

   0.64 s
2. 2.

   On the Moon, a best-fit line of d (m) against t² (s²) has slope 0.81 m/s². How long does a ball take to fall 2 m, to 0.01 s, Bo?

   1.57 s

3. Read this first

   Ball dropped from rest, measured with a sensor (example data)

   time (s)	distance fallen (m)
   0.1	0.05
   0.2	0.19
   0.3	0.45
   0.4	0.79
   0.5	1.22

4. 3.

   Which plot of these measurements gives a straight line, and about what slope, Jun?

   • Distance against time, with a slope near 2.4 m/s
   • Distance against time squared, with a slope near 4.9 m/s²
   • Distance against time squared, with a slope near 9.8 m/s²
   • Time squared against distance, with a slope near 9.8 s²/m
5. 4.

   In this table, the 0.30 s reading looks off. What is the best way to handle it, Luz?

   • Switch to a straight-line fit of d against t, since it fits better
   • Keep it unchanged, since removing any data would be dishonest
   • Delete it, since any point that sits away from the fitted line is an error
   • Recheck that trial: its d ÷ t² is 5.7 where the others are near 4.9

6. Stopping distance of a car on a dry road (example data)

   speed (m/s)	stopping distance (m)
   10	8
   20	32

7. 5.

   Milo says doubling a car's speed doubles its stopping distance. Using the table, agree or disagree?

   • Agree: braking force fixes the distance whatever the speed
   • Disagree: the distance rose from 8 m to 16 m, twice as much
   • Disagree: the distance rose from 8 m to 32 m, four times as much
   • Agree: the speed doubled, so the stopping distance doubles along with it
8. 6.

   Noah says the graph's straight line shows position is directly proportional to time. Agree or disagree?

   • Agree: its slope of 2 m/s is the same everywhere along the line
   • Disagree: the line starts at 3 m, so doubling t does not double x
   • Disagree: a curved graph is needed to show direct proportion
   • Agree: a straight line on a position graph means proportion

9. Light meter readings from a bare lamp (example data)

   distance (m)	reading (units)
   1	16
   2	4
   4	1

10. 7.

    On a log-log graph of the readings the slope is −2.0. Pia says intensity halves when the distance doubles. Agree or disagree?

    • Disagree: slope −2 means doubling the distance divides intensity by 2
    • Agree: a negative slope means that doubling the distance halves it
    • Disagree: slope −2 means doubling the distance divides intensity by 4
    • Agree: the readings fall from 16 to 4, which is halving twice over
11. 8.

    Using the table, which relationship fits the planets' orbits, Ren?

    • T² is proportional to a²; T² ÷ a² is the same for each planet
    • T is proportional to a; T ÷ a is the same for each planet
    • T² is proportional to a³; T² ÷ a³ is about 1.00 for each planet
    • T is proportional to a²; T ÷ a² is the same for each planet

12. Light meter readings from a bare lamp (example data)

    distance (m)	reading (units)
    1	16
    2	4
    4	1

13. 9.

    Which plot of the light readings gives a straight line through the origin, Tala?

    • Reading against distance, with the lamp's strength as the slope
    • Reading against 1/distance, with the lamp's strength as slope
    • Reading against distance², with the lamp's strength as slope
    • Reading against 1/distance², with the lamp's strength as slope
14. 10.

    Zee fits a straight line through these two pendulum points and predicts the period at 4 m. What goes wrong?

    • The line is fine, but the pendulum's length was mismeasured
    • The line predicts 6.0 s at 4 m, but T² ∝ L gives 4.0 s
    • The line is fine, since a line fits any two points exactly
    • The line predicts 3.0 s at 4 m, but T² ∝ L gives 4.0 s