Mechanics, Part 2

Question 1: Describe how position is determined in physics.

Answer 1: In order to determine anything about the motion of an object, we must first locate it. In other words, we must be able to describe its position relative to some reference point, often called an origin. If we consider the origin as the zero point of an axis, then the positive direction of the axis will be the direction in which measuring numbers are getting larger, and the negative direction is that in which the numbers are getting smaller. If a particle is located 5 cm from the origin in the positive direction of the x-axis, its location is said to be x = 5 cm. If another particle is 5 cm from the origin in the negative direction of the x-axis, its position is x = -5 cm. These two particles are 10 cm apart. A vector whose starting point is the origin and whose endpoint is the location of an object is that object’s position vector, with units of length.

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Question 2: Discuss displacement.

Answer 2: When something changes its location from one place to another, it is said to have undergone displacement. If we can determine the original and final position of the object, then we can determine the total displacement with this simple equation: ?x = final position – original position. If the object has moved in the positive direction, then the final position will be greater than the original position, so we can say that the change was positive. If the final position is less than the original, however, displacement will be negative. Displacement along a straight line is a very simple example of a vector quantity: that is, it has both a magnitude and a direction. If an object travels from position x = -5 cm to x = 5 cm, it has undergone a displacement of 10 cm. If it traverses the same path in the opposite direction, its displacement is -10 cm. A vector that spans the object’s displacement in the direction of travel is known as a displacement vector, with units of length.

Question 3: Discuss average velocity.

Answer 3: There are two types of velocity that are commonly considered in physics: average velocity and instantaneous velocity. If we want to calculate the average velocity of an object, we must know two things. First, we must know its displacement, or the distance it has covered. Second, we must know the time it took to cover this distance. Once we have this information, the formula for average velocity is quite simple: vav = (xf – xi)/(tf – ti), where the subscripts i and f denote the intial and final values of the position and time. In other words, the average velocity is equal to the change in position divided by the change in time. This calculation will indicate the average distance that was covered per unit of time. Average velocity is a vector and will always point in the same direction as the displacement vector (since time is a scalar and always positive).

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