Physics 1.3 - Vectors And Scalars

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.

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.

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 =

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.

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.