Find the relationship in a data table and graph

Answer Key - Grade 11 Science Worksheet

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

1. 1.

   A pendulum swings in 1 s at 0.25 m long and 2 s at 1 m long, following a power law. What is its period at 2.25 m, Bo?

   3
2. 2.

   A car needs 7.2 m to stop from 10 m/s and 28.8 m from 20 m/s, following a power law. What distance does it need from 30 m/s, Esme?

   64.8
3. 3.

   Jun plots T² (s²) against L (m) for a pendulum. The line through the origin has slope 4.0 s²/m. Using T = 2π√(L/g), what is g?

   • About 4.0 m/s², since the slope of the line is g
   • About 158 m/s², since g equals 4π² times the slope
   • About 0.10 m/s², since g equals the slope divided by 4π²
   • About 9.9 m/s², since the slope is 4π² ÷ g
4. 4.

   A braking car's stopping distance d follows d = v² ÷ (2a). Which plot is a straight line, and what is its slope, Kira?

   • d against 1/v, with a slope equal to twice the acceleration
   • d against v, with a slope equal to the acceleration a
   • d against v², with a slope of 1 ÷ (2a)
   • v against d, with a slope equal to the acceleration a
5. 5.

   A gas at fixed temperature follows P × V = constant. Which plot of pressure P gives a straight line through the origin, Luz?

   • P against 1/V, with the constant as the slope
   • P against V, with the constant as the slope
   • 1/P against 1/V, with the constant as the slope
   • P against V², with the constant as the slope
6. 6.

   Which plot of the table makes a straight line through the origin, Milo?

   • Period against 1/length, since the longer pendulums are slower
   • Period squared against length
   • Period against length squared, since the periods are rounded
   • Period against length, since both columns rise together
7. 7.

   Pia measured these periods. Do they fit T² = 4L, where T² ÷ L is 4?

   • Yes: T² ÷ L is between 3.9 and 4.2, within about 5% of 4
   • No: T ÷ L falls from 4.1 to 1.4, so there is no pattern
   • Yes: the period rises each time the length rises, so it fits
   • No: no period equals exactly 2√L, so the model fails
8. 8.

   A spring's stretch (m) against force (N) has slope 0.02 m/N. What is its spring constant k, the force per meter, Ren?

   • 50 N/m, since k is the inverse of the slope
   • 0.02 m/N, since the slope already has k's units
   • 0.02 N/m, since k equals the slope
   • 5 N/m, since k is the slope divided by 10
9. 9.

   Force (N) plotted against acceleration (m/s²) for a cart gives slope 2.5. What does the slope mean, Tala?

   • The cart's weight: 2.5 N
   • The cart's inverse mass: 2.5 per kg
   • The cart's mass: 2.5 kg
   • The cart's speed: 2.5 m/s
10. 10.

    The slopes of a position-time curve at 2 s and 6 s are 2 m/s and 6 m/s. What does (6 − 2) ÷ (6 − 2) tell Zee?

    • The average velocity: 1 m/s
    • The average acceleration: 4 m/s²
    • The distance moved: 4 m
    • The average acceleration: 1 m/s²