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Main Kinematics & Dynamics Distance & Displacement Lesson I.3.1 Unit I:Kinematics & Dynamics

Distance and Displacement - Lesson I.3.1

Key Terms:

position | distance | displacement | IL, CCT, NUM

In order to study kinematics we need to understand three basic terms: position, displacement, and distance.

Position, postion vector symbol, is the location of an object relative to a reference point. It is a vector quantity and as such needs a magnitude and direction.

Displacement, displacement vector symbol, can be described as the change in position of an object. It is the straight line segment that connects the initial and final positions. Displacement is also a vector quantity and therefore needs a magnitude and direction.

Distance, distance symbol, is the length of the path traveled by an object as it moves from one point to another. It is a scalar quantity and therefore only needs to be described using a magnitude.

The SI unit for position, displacement, and distance is the meter (m).

Distance vs. Displacement

The position or change in position of an object in one dimension (i.e. collinear vectors) can be described using a number line. In order to determine direction, positive and negative numbers relative to the origin are used. North-south directions are not used since the line may not run that way and left-right may be confusing depending on the position of the observer.

Number Line

When using a number line you would calculate the displacement of your object as it moved from position x1 to x2 by the difference between the later position and the initial position. x2 - x1 = +4 - (-3) =+7

The displacement can either be positive or negative depending on the direction of the motion.

        x2 - x1 = 0 - (-3) = 3
        x2 - x1 = 0 - (-3) = 3
        x2 - x1 = -1 - 4 = - 5

        x2 - x1 = 2 - (-1) = 3

In the above examples both a), b), and d) are equivalent displacements since they have the same magnitude and direction. Equivalent displacements do not need to have the same origin.

In your previous lesson, you were asked to calculate the resultant vector for a group of non-collinear vectors. Since all problems dealt with a change in position of an object, you were also calculating the resultant displacement of an object.

Now let's do a problem using distance, displacement and position.

In a swimming race, Cynthia swam 2.5 km [E] followed by 7.0 km [S 21 E]. Calculate:

  1. the total distance traveled
  2. Cynthia's resultant displacement
  3. Cynthia's final position

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