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. 3.

   On Mars, a best-fit line of d (m) against t² (s²) has slope 1.855 m/s². How long does a ball take to fall 3 m, to 0.01 s, Esme?

   1.27 s

4. 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

5. 4.

   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 9.8 m/s²
   • Distance against time squared, with a slope near 4.9 m/s²
   • Time squared against distance, with a slope near 9.8 s²/m
6. 5.

   Kira plots log d against log t for a falling ball and gets a straight line of slope 2.0. What does that show?

   • Distance is proportional to √t, since logarithms undo squares in the data
   • Distance is proportional to 2t, since the slope of the line is 2.0 exactly
   • Distance is proportional to t², since the log-log slope is the exponent
   • Distance is proportional to t, since the line on the graph is straight

7. 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	0.51
   0.4	0.79
   0.5	1.22

8. 6.

   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
   • Recheck that trial: its d ÷ t² is 5.7 where the others are near 4.9
   • 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

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

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

10. 7.

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

    • Agree: the speed doubled, so the stopping distance doubles along with it
    • Disagree: the distance rose from 8 m to 16 m, twice as much
    • Agree: braking force fixes the distance whatever the speed
    • Disagree: the distance rose from 8 m to 32 m, four times as much
11. 8.

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

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

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

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

13. 9.

    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: the readings fall from 16 to 4, which is halving twice over
    • Agree: a negative slope means that doubling the distance halves it
    • Disagree: slope −2 means doubling the distance divides intensity by 4
14. 10.

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

    • 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
    • T² is proportional to a²; T² ÷ a² is the same for each planet
    • T is proportional to a²; T ÷ a² is the same for each planet