Position-time and velocity-time graphs

Answer Key - Grade 11 Science Worksheet

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

1. 1.

   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.

   15 m

2. Read this first

   A cart's velocity (example data)

   time (s)	velocity (m/s)
   0	0
   1	1
   2	4
   3	9
   4	16

3. 2.

   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?

   • 32 m: ½ × 16 m/s × 4 s, treating the curve as straight
   • About 22 m: 0.5 + 2.5 + 6.5 + 12.5
   • 30 m: 0 + 1 + 4 + 9 + 16, one second each
   • 64 m: 16 m/s × 4 s, using the final velocity
4. 3.

   Kira estimates the cart's acceleration at 2 s from the table. The acceleration is not constant. Which estimate is best?

   • 4 m/s²: (9 − 1) ÷ (3 − 1), from both sides
   • 2 m/s²: 4 ÷ 2, the average since the start
   • 5 m/s²: (9 − 4) ÷ 1, from the second after
   • 3 m/s²: (4 − 1) ÷ 1, from the second before
5. 4.

   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
   • It speeds up with shrinking acceleration: 4, 3, 2, then 1 m/s²
   • Its acceleration grows, since the velocity grows each second
   • It stops accelerating at 3 s, since the gains get smaller
6. 5.

   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 0.5 m/s; average speed 3.5 m/s
   • Average velocity 1.2 m/s; average speed 3.6 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
7. 6.

   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?

   • At its start, 0 m
   • 3 m above its start
   • 21 m above its start
   • 3 m below its start
8. 7.

   Pia reads the velocity-time graph. When does the cart stop, and how far is it from its start then?

   • At 3 s, 3 m from the start, where the line ends
   • At 2 s, 4 m from the start
   • At 2 s, 8 m from the start (4 m/s × 2 s)
   • At 1.5 s, 3 m from the start
9. 8.

   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
10. 9.

    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 25.5 m
    • Displacement 28.5 m; distance 25.5 m
    • Displacement 25.5 m; distance 28.5 m
    • Displacement 21 m; distance 21 m, counting the first two pieces
11. 10.

    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
    • 4 m/s: 2 + 2 × 3 − 1 × 4
    • 8 m/s, the velocity at 3 s