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.
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?
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?
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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 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
- Distance against time, with a slope near 2.4 m/s
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 2t, since the slope of the line is 2.0 exactly
- Distance is proportional to √t, since logarithms undo squares in the data
- 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
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?
- Keep it unchanged, since removing any data would be dishonest
- Recheck that trial: its d ÷ t² is 5.7 where the others are near 4.9
- Switch to a straight-line fit of d against t, since it fits better
- Delete it, since any point that sits away from the fitted line is an error
Noah says the graph's straight line shows position is directly proportional to time. Agree or disagree?
- 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: its slope of 2 m/s is the same everywhere along the line
- Agree: a straight line on a position graph means proportion
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?
- 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 2
- Disagree: slope −2 means doubling the distance divides intensity by 4
Using the table, which relationship fits the planets' orbits, Ren?
- 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
- T² is proportional to a²; T² ÷ a² 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/distance², with the lamp's strength as slope
- Reading against 1/distance, with the lamp's strength as slope
- Reading against distance², with the lamp's strength as slope
- Reading against distance, with the lamp's strength as the 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