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 9 m/s forward to 3 m/s backward in 4 s. What is its displacement over that time, Bo? 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 Kira estimates the cart's acceleration at 2 s from the table. The acceleration is not constant. Which estimate is best?
- 3 m/s²: (4 − 1) ÷ 1, from the second before
- 5 m/s²: (9 − 4) ÷ 1, from the second after
- 4 m/s²: (9 − 1) ÷ (3 − 1), from both sides
- 2 m/s²: 4 ÷ 2, the average since the start
Luz reads the cart's velocity table. Which statement about its acceleration is right?
- It speeds up at a steady 2.5 m/s², the average over 4 s
- Its acceleration grows, since the velocity grows each second
- It speeds up with shrinking acceleration: 4, 3, 2, then 1 m/s²
- It stops accelerating at 3 s, since the gains get smaller
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?
- 3 m below its start
- At its start, 0 m
- 3 m above its start
- 21 m above its start
Pia reads the velocity-time graph. When does the cart stop, and how far is it from its start then?
- At 1.5 s, 3 m from the start
- 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
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
- +8 m/s, then 0, then +2 m/s, using the positions
- +2 m/s, then +2 m/s, then −1.5 m/s
- +2 m/s, then 0, then +1.5 m/s, using speeds
Tala reads the velocity-time graph. What are the cart's displacement and total distance from 0 s to 8 s?
- Displacement 21 m; distance 21 m, counting the first two pieces
- Displacement 25.5 m; distance 28.5 m
- Displacement 25.5 m; distance 25.5 m
- Displacement 28.5 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?
- 10 m/s: 2 + 6 + 4, counting both areas as gains
- 6 m/s: 2 + 2 × 3 − 1 × 2
- 8 m/s, the velocity at 3 s
- 4 m/s: 2 + 2 × 3 − 1 × 4