Position-time and velocity-time graphs
Grade 11 Science Worksheet
Circle the best answer, or write your answer on the line.
A cart's velocity falls steadily from 6 m/s forward to 2 m/s backward in 4 s. What is its displacement over that time, Ari? Forward is positive.
A cart's velocity falls steadily from 8 m/s forward to 2 m/s backward in 5 s. What is its displacement over that time, Esme? Forward is positive.
Read this first
A cart's velocity (example data)
time (s) velocity (m/s) 0 0 1 1 2 4 3 9 4 16 Jun estimates the cart's displacement over the first 4 s from the velocity table, using one trapezoid for each second. What does Jun get?
- 30 m: 0 + 1 + 4 + 9 + 16, one second each
- About 22 m: 0.5 + 2.5 + 6.5 + 12.5
- 64 m: 16 m/s × 4 s, using the final velocity
- 32 m: ½ × 16 m/s × 4 s, treating the curve as straight
Kira estimates the cart's acceleration at 2 s from the table. The acceleration is not constant. Which estimate is best?
- 5 m/s²: (9 − 4) ÷ 1, from the second after
- 4 m/s²: (9 − 1) ÷ (3 − 1), from both sides
- 3 m/s²: (4 − 1) ÷ 1, from the second before
- 2 m/s²: 4 ÷ 2, the average since the start
A cart rolls forward at 4 m/s for 6 s, then backward at 3 m/s for 4 s. What are its average velocity and average speed over the 10 s, Milo?
- Average velocity 1.2 m/s; average speed 3.6 m/s
- Average velocity 0.5 m/s; average speed 3.5 m/s
- Average velocity 3.6 m/s; average speed 1.2 m/s
- Average velocity 3.6 m/s; average speed 3.6 m/s
A drone rises at 3 m/s for 4 s, hovers for 2 s, then descends at 1.5 m/s for 6 s. Where is it compared with its start, Noah?
- 21 m above its start
- 3 m above its start
- 3 m below its start
- At its start, 0 m
Pia reads the velocity-time graph. When does the cart stop, and how far is it from its start then?
- At 2 s, 8 m from the start (4 m/s × 2 s)
- At 3 s, 3 m from the start, where the line ends
- At 2 s, 4 m from the start
- At 1.5 s, 3 m from the start
Ren turns the position-time graph into a velocity-time graph. Which set of velocities is right?
- +2 m/s, then 0, then −1.5 m/s; the sign changes at 6 s
- +2 m/s, then +2 m/s, then −1.5 m/s
- +2 m/s, then 0, then +1.5 m/s, using speeds
- +8 m/s, then 0, then +2 m/s, using the positions
Tala reads the velocity-time graph. What are the cart's displacement and total distance from 0 s to 8 s?
- Displacement 25.5 m; distance 28.5 m
- Displacement 21 m; distance 21 m, counting the first two pieces
- Displacement 28.5 m; distance 25.5 m
- Displacement 25.5 m; distance 25.5 m
A cart starts at 2 m/s. Zee reads its acceleration-time graph. What is the cart's velocity at 7 s?
- 6 m/s: 2 + 2 × 3 − 1 × 2
- 4 m/s: 2 + 2 × 3 − 1 × 4
- 8 m/s, the velocity at 3 s
- 10 m/s: 2 + 6 + 4, counting both areas as gains