Physics 1.3 - Vectors And Scalars - Quiz, Flashcards & Trivia

1. Which of the follwing is not a scalar?

Speed

Work

Displacement

Temperature

Speed only describes how fast an object moves but not the direction. So it is a scalar. A is incorrect.

Work describes how much energy a force changes. It is a scalar as the energy. B is incorrect.

Distance is the path length, and it is a scalar. But displacement indicates the direction is from the starting point to the ending point, so it is a vector.

Temperature describes how warm an object is and it has only magnitude and no direction. So temperature is scalar. D is incorrect.

Explanation

Speed only describes how fast an object moves but not the direction. So it is a scalar. A is incorrect.

Work describes how much energy a force changes. It is a scalar as the energy. B is incorrect.

Distance is the path length, and it is a scalar. But displacement indicates the direction is from the starting point to the ending point, so it is a vector.

Temperature describes how warm an object is and it has only magnitude and no direction. So temperature is scalar. D is incorrect.

2. A person walks 4 km north, and then walks 8 km west, and then he walks 2km north. How far away is he from his starting point?

14km

2km

8km

10km

The above graph shows the person walking. The red vector is the sum of the three blue vectors and we are looking for its magnitude. We can calculate the magnitude by drawing the dash lines, then the red line is the hypotenuse of the right triangle with one side 6 km and the other side 8 km.

We can use the Pythagorean theorem to calculate the length.

lenght =

Explanation

The above graph shows the person walking. The red vector is the sum of the three blue vectors and we are looking for its magnitude. We can calculate the magnitude by drawing the dash lines, then the red line is the hypotenuse of the right triangle with one side 6 km and the other side 8 km.

We can use the Pythagorean theorem to calculate the length.

lenght =

3. Which of the following is not a vector?

Area

Weight

Electric field

Volume

Area is a vector; the direction of an area is perpendicular to the surface. So A is incorrect. Weight is a vector. It is a type of force; the direction of the force is downward on Earth’s surface. So B is incorrect. Electric field is a vector, the direction of which is the same as the force felt by a positive charge. So C is incorrect.

Explanation

Area is a vector; the direction of an area is perpendicular to the surface. So A is incorrect. Weight is a vector. It is a type of force; the direction of the force is downward on Earth’s surface. So B is incorrect. Electric field is a vector, the direction of which is the same as the force felt by a positive charge. So C is incorrect.

4. If the initial velocity vector is 3 m/s to the east, and the final velocity vector is 3 m/s to the south, what is the change in velocity?

0 m/s

6 m/s to the southeast

4.2 m/s to the southeast

4.2 m/s to the southwest

The change of velocity is equal to the final velocity subtracted by the initial velocity, which is equal to the final velocity add the negative initial velocity. We can calculate the change using the Pythagorean theorem = =

The direction is southwest as shown in the graph.

Explanation

The change of velocity is equal to the final velocity subtracted by the initial velocity, which is equal to the final velocity add the negative initial velocity. We can calculate the change using the Pythagorean theorem = =

The direction is southwest as shown in the graph.

5. A person is dragging a box to the left upward with a force of 10 N. The force forms angle of 60 degrees with the horizontal. What is the horizontal and vertical component of this force if we choose the upward and the right to be the positive direction?

Horizontal 5N Vertical 8.7N

Horizontal 8.7N Vertical 5N

Horizontal 5N Vertical 5N

We can see in the graph that the horizontal component is the adjacent side of the 60 degree angle, so we can use cosine and the vertical component is the opposite side of the 60 degree angle, so we can use sine.

horizontal component =

vertical component =

Then we notice that the horizontal component is to the left, which is opposite of the direction we define as positive. So the correct answer is -5N for horizontal component. The vertical component is positive, and it is 8.7N.

Explanation

We can see in the graph that the horizontal component is the adjacent side of the 60 degree angle, so we can use cosine and the vertical component is the opposite side of the 60 degree angle, so we can use sine.

horizontal component =

vertical component =

Then we notice that the horizontal component is to the left, which is opposite of the direction we define as positive. So the correct answer is -5N for horizontal component. The vertical component is positive, and it is 8.7N.