Most students will be familiar with scalars, but to many, vectors may be a new and confusing concept. By learning just a few rules for dealing with vectors, though, you’ll find that they are a powerful tool for problem solving.

      A study of motion involves introduction of a variety of quantities that are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity, acceleration, force, mass, momentum, energy, work, power, etc. All these quantities can by divided into two categories – vectors and scalars. A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions.

      Examples of vector quantities include displacement, velocity, acceleration, and force. Each of these quantities is unique in that a full description of the quantity demands that both a magnitude and a direction are listed. For example, suppose your teacher tells you, «A bag of gold is located outside the classroom. To find it, displace yourself 20 meters». This statement may provide you enough information to pique your interest; yet, there is not enough information included in the statement to find the bag of gold. The displacement required to find the bag of gold has not been fully described. On the other hand, suppose your teacher tells you, «A bag of gold is located outside the classroom. To find it, displace yourself from the center of the classroom door 20 meters in a direction 30 degrees to the west of north». This statement now provides a complete description of the displacement vector – it lists both magnitude (20 meters) and direction (30 degrees to the west of north) relative to a reference or starting position (the center of the classroom door). Vector quantities are not fully described unless both magnitude and direction are listed.

      Vectors are often represented as arrows, with the length of the arrow indicating the magnitude of the quantity, and the direction of the arrow indicating the direction of the vector. In the figure at right, vector B has a magnitude greater than that of vector A. Vectors A and B point in the same direction, however. It’s also important to note that vectors can be moved anywhere in space. The positions of A and B could be reversed, and the individual vectors would retain their values of magnitude and direction. This makes adding vectors very straight forward!

      To add vectors A and B, all we have to do is line them up so that the tip of the first vector touches the tail of the second vector. Then, to find the sum of the vectors, known as the resultant, all we have to do is draw a straight line from the start of the first vector to the end of the last vector. This method works with any number of vectors.

      Velocity and speed are very similar ideas, but velocity is a vector, and speed is not. Suppose we knew that someone was driving at thirty-five kilometers an hour (35 km/hr), but the direction wasn't given. How would you draw an arrow to represent a vector? You can't know how to draw the vector if you only have one value (either amount or direction). In this example, you were never told about the direction. Physicists would say that the speed is thirty-five kilometers an hour (35 km/hr), but the velocity is unknown. On the other hand, if you're moving at 35 km/hr in a northern direction, then you would have an arrow pointing north with a length of 35. Physicists would say that the velocity is 35 km/hr north.

      Velocity is the rate of motion in a specific direction. I'm going that-a-way at 30 kilometers per hour. My velocity is 30 kilometers per hour that-a-way. Average speed is described as a measure of distance divided by time. Velocity can be constant, or it can change (acceleration). Speed with a direction is velocity.

      You will use a lot of vectors when you work with velocity. Our real world example of navigation on the ocean used velocity for every vector. Velocity is a vector measurement because it has an amount and a direction. Speed is only an amount (a scalar). Speed doesn't tell the whole story to a physicist. Think of it another way. If I tell you I'm driving north and ask you how long until we get to the city. You can't know the answer since you don't know my speed. You need both values.

      When velocity is changing, the word acceleration is used. Acceleration is also a vector. You speed up if the acceleration and velocity point in the same direction. You slow down (also referred to as decelerating) if the acceleration and velocity point in opposite directions. When you accelerate or decelerate, you change your velocity by a specific amount over a specific amount of time. Just as with velocity, there is something called instantaneous acceleration. Instantaneous means scientists measure your acceleration for a specific moment of time. That way they can say he was accelerating at exactly this amount at this point during his trip.

      VII. Answer the questions on the text

      1. Why do physicists use quantities?

      2. What do we mean by ‘scalars’?

      3. What examples do scalars include?

      4. A motorboat, which has a speed of 5.0 meters per second in still water, is headed east as it crosses a river flowing south at 3.3 meters per second. What is the magnitude of the boat's resultant velocity with respect to the starting point?

      3.3 m/s

      5.0 m/s

      6.0 m/s

      8.3 m/s

      UNIT 5

      Vocabulary

      earth n. – Земля;

      source n. – источник;

      solar a. – солнечная система;

      hydroelectric a. – гидроэлектрический;

      fossil n. – ископаемое;

      fuel n. – топливо;

      trace v. – оставить след;

      origin n. – 1) возникновение; 2) происхождение;

      investigate v. – 1) исследовать; 2) расследовать;

      motion n. – движение;

      to develop v. – 1) развивать,