Distance and displacement

Run one full lap of a four hundred metre running track, and stop on the line you started from. Your distance is four hundred metres. Your displacement is zero. Both answers are correct, and an exam question can ask you for either one.

You are on video three of six in Units and describing motion, and it is for combined science and triple physics, Foundation and Higher tiers both. If today feels shaky, Scalars and vectors is the one to watch first.

Distance is the total length of the path you actually travelled. It is a scalar, so it has no direction, and it can never be negative. Displacement is the straight line from where you started to where you finished. It is a vector, so it needs a size and a direction. Both are measured in metres. The unit cannot tell you which one you are holding, so the words in the question have to. A student walks sixty metres east along a corridor, then turns and walks twenty-five metres back west. Distance first. Add up every metre walked: sixty plus twenty-five is eighty-five metres. Displacement: eighty-five metres, thirty-five metres, or thirty-five metres east? Thirty-five metres east. Eighty-five is the distance, and thirty-five with no direction is only half a vector. Sixty out and twenty-five back leaves the student thirty-five metres from the start. The straight arrow from start to finish is thirty-five metres long, and it points east.

An athlete runs three complete laps of a four hundred metre track, and stops on the start line. The distance is three times four hundred, which is one thousand two hundred metres. What is the athlete's displacement after those three complete laps? Zero. The start and the finish are the same point, so the straight arrow between them has no length at all. But the athlete definitely moved. That is true, and it is exactly what the distance records. Displacement only asks how far the finish is from the start, and here that is nothing. Your handle for this video is two pictures: the traced path for distance, and the straight arrow from start to finish for displacement.

A drone flies three hundred metres north, then four hundred metres further north. Both legs point the same way, so the whole path is one straight line. The distance is three hundred plus four hundred, which is seven hundred metres. The displacement is seven hundred metres north. On a straight trip in one direction, the two sizes match. Now change only the second leg, and send it the opposite way. Three hundred north, then four hundred south: what are the distance and the displacement? The distance is still seven hundred metres. The displacement is one hundred metres south, because the drone ends up one hundred metres south of where it started. The distance did not notice the change of direction at all. The displacement changed completely, size and direction both, and that is what a vector does.

Someone answers a displacement question with two hundred and fifty metres, and nothing else. What is wrong with the answer two hundred and fifty metres? It has no direction, so it is only half an answer. Two hundred and fifty metres north and two hundred and fifty metres south are both possible, and they describe opposite journeys. One examiner's report on a Higher paper records this, about a question whose answer was a kind of quantity. The majority of candidates gave the answer of scalar although a few candidates gave the answer of vector, displacement or speed. Scalar and vector are the names of the two groups. Distance, displacement and speed are quantities that sit inside them. The fix is to answer a which-kind question with the group's name, never a quantity's.

Time to test all of that on journeys this video has not used. A dog runs forty metres to a ball and back. What are both answers to how far? Eighty metres of distance, and zero displacement, because the dog finishes where it started. Now a lift: up twelve metres, then down four. Distance and displacement? Sixteen metres of distance. The displacement is eight metres upwards. One more. Which can be bigger, distance or displacement, and when are they equal? Distance can be bigger. The two sizes are equal only when the trip is a straight line in one direction. And the four hundred metre track: four hundred metres of distance, a displacement of zero, and both correct. The word in the question tells you which one it wants.

Once this is in the bag, hit the thumb, so your list of videos without one shows what is left to revisit. If it is still wobbly, save it and give it a day; it often settles once you look again tomorrow.

Next in the chapter: Speed, typical speeds and s equals v t, where a time finally joins the distance.

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