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Lesson Worksheet: Vector Quantities Mathematics

In this worksheet, we will practice describing how vectors are used in mechanics to solve problems in two dimensions.

Q1:

Consider the list:

  1. Displacement
  2. Distance
  3. Acceleration
  4. Velocity
  5. Speed

Select all of the list items that are vector quantities.

  • AI and IV
  • BIV and V
  • CII, III, and V
  • DI, III, and IV
  • EII, III, and IV

Q2:

Say that the positive direction of motion is toward the right. Which of the following correctly describes the motion of a particle whose velocity is negative and acceleration is positive?

  • AThe particle is slowing down while it is moving to the left.
  • BThe particle is speeding up while it is moving to the right.
  • CThe particle is speeding up while it is moving to the left.
  • DThe particle is slowing down while it is moving to the right.

Q3:

The car is traveling on a highway along the route shown.

The distance between points A and B is 60 km, and the distance between points B and C is 30 km. The car travels from A to C, passing through B, and then back to A, passing through B. Within each segment, the car travels at a constant speed of 90 km/h. What is the displacement of the car from C to B? Also, what is the velocity of this segment?

  • A60 km, 90 km/h
  • B60 km, 90 km/h
  • C30 km, 90 km/h
  • D30 km, 90 km/h
  • E30 km, 90 km/h

Q4:

A particle is moving from point 𝐴 to point 𝐵 and then to point 𝐶. The displacement from point 𝐴 to point 𝐵 is 3+5ij cm, and the displacement from point 𝐵 to point 𝐶 is ij7 cm. Find the distance between point 𝐴 and point 𝐶 rounded to the nearest one-hundredth of a centimeter.

Q5:

The velocity of a particle is 43ij m/s. Find the speed of the particle.

Q6:

The velocity of a particle is 43ij m/s. Find the angle, rounded to the nearest degree, that the motion of this particle makes with the unit vector i.

Q7:

The acceleration of a particle is 43ij m/s2. Find the magnitude of acceleration of the particle.

Q8:

The acceleration of a particle is 43ij m/s2. Find the angle, rounded to the nearest degree, that the acceleration of this particle makes with the unit vector i.

Q9:

A particle is moving from point 𝐴 to point 𝐵 and then to point 𝐶. The displacement from point 𝐴 to point 𝐵 is 3+5ij cm, and the displacement from point 𝐵 to point 𝐶 is ij7 cm. Find the total distance traveled by this particle in centimeters, rounded to the nearest tenth.

Q10:

The displacement from point 𝐴 to point 𝐵 is 3+5ij cm. Find the angle, rounded to the nearest degree, that the trajectory of this particle makes with the unit vector j.

This lesson includes 72 additional question variations for subscribers.

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