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11th grade Position-time and velocity-time graphs worksheet

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Position-time and velocity-time graphs

Grade 11 Science Worksheet

NameDate

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

  1. 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.

  2. 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.

  3. 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.

  4. Read this first

    A cart's velocity (example data)

    time (s)velocity (m/s)
    00
    11
    24
    39
    416

  5. 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?

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

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

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

  7. 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 3.6 m/s; average speed 3.6 m/s
    • 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

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

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

    • At 2 s, 4 m from the start
    • 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

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

  11. 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
    • 4 m/s: 2 + 2 × 3 − 1 × 4
    • 6 m/s: 2 + 2 × 3 − 1 × 2
    • 8 m/s, the velocity at 3 s
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11th grade Position-time and velocity-time graphs worksheet – printable
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About this worksheet

Position-time and velocity-time graphs. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can turn a position-time graph into its velocity-time graph: a straight rising line gives a flat line above zero, a flat line gives zero, and a falling line gives a flat line below zero.
  • I can read slope and area. Position-time slope is velocity, velocity-time slope is acceleration, and velocity-time area is displacement (rectangle, triangle or trapezoid; negative below zero).
  • I can read a curved position-time line: getting steeper means speeding up, and the tangent's slope is the instantaneous velocity.

Standard: supports HS-PS2-1

Words to know

slope: Rise ÷ run on a graph

area under the line: The space between the line and zero, here a displacement

tangent: A straight line touching a curve at one point

instantaneous velocity: Velocity at one moment: the tangent's slope

average velocity: Total displacement ÷ total time

Common mistakes

Your child added the sizes of the motions. Displacement counts a backward motion as negative; distance counts every part as positive.

Your child left out the backward motion. Displacement includes every part of the trip, with backward parts negative.

Your child used the starting velocity for the whole time. The velocity changes steadily, so use the average, or add the signed areas.

Questions parents ask

What is the most common mistake with position-time and velocity-time graphs?

Your child added the sizes of the motions. Displacement counts a backward motion as negative; distance counts every part as positive.

Are these 11th grade science worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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