Displacement vs. Distance

== Distance vs. Displacement== Distance is a scalar quantity which refers to "How much ground has a motion covered?" Displacement can be said to be the "vector" quantity of distance, but always there is confusion between the two because of their defintion. Displacement refers to the overall change in position of an object from a frame of reference.

The object on the left shows clearly the difference between distance and displacement. The purple line represents the path taken by an object from the frame of reference (starting point). The measurement of the purple path is the distance travelled. But displacement is simply measured from the frame of reference to the end point. In other words it is the "shortest" path possible to get from the starting point to the end point. Since displacement is a vector, it must always show both the magnitude and direction. E.g. The ball was displaced 5m[N]. Directions for a vector quantity are always written inside square ([]) brackets.

The notation for distance in IB is an "S" and the notation for displacement in IB is "S".

Calculating Distance and Displacement
Question: Bob walks 3 metres north, and then walks 4 metres east. What is his distance and displacement?

Answer: Calculating distance is easy in this case. All you have to do is add the two quantities. 3+4=7 therefore the distance that Bob travelled is 7m. Now for displacement. Remember how displacement is the change in position.

As you can see on the diagram, displacement is the shortest distance from the "frame of reference" to the destination point. The solid lines represent the path of Bob while the dotted line represents the shortest path (displacement). Using the Pythagorean theorem, we can find the magnitude of displacement which is square root of 3^2+4^2 which is 5. But to fully complete the question, we must also indicate the angle theta which is the angle between the frame of reference with 3km[N] and magnitude of displacement which is 5m in length. Using SOH CAH TOA, we can find theta. In this case we can use SOH (sin opposite over hypotenuse) or CAH (cosine adjacent over hypotenuse) or even TOA (tan opposite over adjacent) because we know all the sizes of the lines and we know that the triangle is a right angled triangle. We'll use TOA. (tanθ=4m/3m) > θ= 53 degrees. The final answer for the displacement of Bob's movement is 5 m [3km 53degrees 5km]. Later on in IB you would learn a simpler method in indicating the direction using the CAST rule.