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11th grade Scalars and vectors worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Scalars and vectors

Grade 11 Science Worksheet - Building Confidence

NameDate

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

  1. Two tugboats pull a barge with forces of 300 N and 400 N at right angles to each other. What is the size of the net force, Ari?

  2. Two tugboats pull a barge with forces of 50 N and 120 N at right angles to each other. What is the size of the net force, Bo?

  3. Two tugboats pull a barge with forces of 200 N and 210 N at right angles to each other. What is the size of the net force, Esme?

  4. A cart rolling east at 5 m/s slows to 2 m/s, still rolling east. What is the change in its velocity, Kira?

    • 7 m/s west
    • 7 m/s east
    • 3 m/s east
    • 3 m/s west

  5. A skater moving north at 4 m/s turns and moves east at 3 m/s. What is the size of the change in velocity, Luz?

    • 3 m/s
    • 7 m/s
    • 1 m/s
    • 5 m/s

  6. Noah runs half a lap round a circular track 100 m across. The track is 314 m round. What are the distance and the displacement?

    • 314 m and 0 m
    • 100 m and 157 m
    • 157 m and 157 m
    • 157 m and 100 m

  7. Pia rides in a car that drives 60 km north in 1 h, then 80 km east in 1 h. What are its average speed and average velocity?

    • 70 km/h and 50 km/h
    • 35 km/h and 25 km/h
    • 70 km/h and 70 km/h
    • 50 km/h and 50 km/h

  8. Read this first

    Use this

    Arrow grid (example data).

  10. In the arrow grid, what speed does arrow A show, Ren?

    • 10 m/s
    • 7 m/s
    • 14 m/s
    • 5 m/s

  11. Which statement about arrows A and B is right, Tala?

    Use the picture in question 8.

    • They are equal vectors, since both are 10 m/s long
    • A + B is 20 m/s, since both are 10 m/s
    • They are opposite vectors: the same size and opposite directions, so A + B = 0
    • They have different sizes, since B points south and west

  12. How does arrow C compare with arrow A, Zee?

    Use the picture in question 8.

    • The same size as A, but a different direction
    • A different direction from A, and 20 m/s long
    • Same direction as A and twice the size, 20 m/s
    • The same direction as A, but 28 m/s long
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11th grade Scalars and vectors worksheet – printable
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About this worksheet

Scalars and vectors. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the net force of two forces at right angles (a right triangle), and the change in velocity when a ball rebounds or a car turns.
  • I can tell distance from displacement and average speed from average velocity on laps, circles and two-leg trips.
  • I can read an arrow grid with a scale in two directions, and tell equal, opposite and double vectors.
  • I can add velocities for boats, planes and relative motion, find a balancing force, and judge claims about vector sums.

Standard: supports HS-PS2-1

Words to know

scalar: A quantity with size only

vector: A quantity with size and direction

magnitude: The size of a vector, without its direction

displacement: Straight-line change in position, start to finish, with direction

velocity: Displacement per second; speed with a direction

net force: All the forces on an object added as vectors

resultant: The single vector equal to two or more vectors added

relative velocity: One object's velocity as seen from another: subtract their velocities

Common mistakes

Your child added the sizes of two vectors. Vectors that do not point the same way add by their directions, so the sum is shorter than the sizes added.

Your child subtracted the sizes. Only forces pulling opposite ways partly cancel; forces at right angles do not.

Your child subtracted the two speeds. Change in velocity uses the vectors, so reversing direction makes the change larger.

Questions parents ask

What is the most common mistake with scalars and vectors?

Your child added the sizes of two vectors. Vectors that do not point the same way add by their directions, so the sum is shorter than the sizes added.

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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