Find the relationship in a data table and graph
Grade 11 Science Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
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?
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?
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 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
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 t², since the log-log slope is the exponent
- Distance is proportional to t, since the line on the graph is straight
- 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
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 In this table, the 0.30 s reading looks off. What is the best way to handle it, Luz?
- Recheck that trial: its d ÷ t² is 5.7 where the others are near 4.9
- Delete it, since any point that sits away from the fitted line is an error
- Switch to a straight-line fit of d against t, since it fits better
- Keep it unchanged, since removing any data would be dishonest
Stopping distance of a car on a dry road (example data)
speed (m/s) stopping distance (m) 10 8 20 32 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
- 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
- Disagree: the distance rose from 8 m to 32 m, four times as much
Light meter readings from a bare lamp (example data)
distance (m) reading (units) 1 16 2 4 4 1 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
- Disagree: slope −2 means doubling the distance divides intensity by 4
- Agree: a negative slope means that doubling the distance halves it
Using the table, which relationship fits the planets' orbits, Ren?
- T² is proportional to a²; T² ÷ a² 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
- T is proportional to a; T ÷ a is the same for each planet
Light meter readings from a bare lamp (example data)
distance (m) reading (units) 1 16 2 4 4 1 Which plot of the light readings gives a straight line through the origin, Tala?
- Reading against 1/distance, with the lamp's strength as slope
- Reading against distance, with the lamp's strength as the slope
- Reading against 1/distance², with the lamp's strength as slope
- Reading against distance², with the lamp's strength as slope
Zee fits a straight line through these two pendulum points and predicts the period at 4 m. What goes wrong?
- The line is fine, since a line fits any two points exactly
- The line predicts 6.0 s at 4 m, but T² ∝ L gives 4.0 s
- The line predicts 3.0 s at 4 m, but T² ∝ L gives 4.0 s
- The line is fine, but the pendulum's length was mismeasured