text: physical sciene question.? 1.   explain how you arrived at the answer in the case of a numerical problem. (the process is much more important than the answer, and there is not always one 'right' way to arrive at the answer.).  1a.   what is the difference between distance and displacement?   1b.  give an example of each (distance and displacement).    2.    jack and jill set out for a morning run. they both run 2 miles north along rte 3 and then turn and run back south to home (to the starting point). jill stops at home, but jack continues to run south for an additional 3 miles to the gym.   a.    how far did jill run? (remember the defintion of distance.)  b.    what was the displacement for her entire run? (remember the definition of displacement.)  c.    how far did jack run? (remember the definition of distance.)  d.    what was the displacement for his entire run? (remember the definition of displacement.) first off, distance is a measure of length. when you say that an object is 1 inch long, you are measuring the distance from one of it to the other.  when you hear that a space object is x light years from earth, the x light years also represent distance, specifically the number of kilometers light will travel in that amount of time. since light is so fast that it travels about 186,000 miles per second & since space is so large, it is more convenient to measure distance in space using the distance (the # of miles) light will travel in 1 year then multiply that by a number of years that will give you at least an estimate of how far that object is from earth.  while distance is a measurement, displacement, on the other hand, is a rate. when you hear a car was going 100 miles an hour, that is a rate. a 100 miles between two given cities is just the distance between them. but travelling (on foot, on a bicycle, on a motorcycle, by car, by train, by boat, by plane or by any other means) x units of distance (10 kilometers, 300 miles, 50 yards, 2 inches etc.) in y units of time (30 seconds, 4 minutes, 5 hours, 6 days, 9 weeks, 8 months, 2 years, 1 decade (= 10 years), 4 centuries (1 century = 100 years), or 3 millenia (1 millenium = 1000 years)) then that is a rate.  displacement is a rate of change, not merely a ratio between two things, such as a ratio of distance to time. displacement indicates the change in position, relative to the point of origin & the destination.  in the example you provide, if jill moves from point a to point b, then she has travelled a distance of x units, x being the length between them. if she moves from point a to point b then back, then she went back over the distance she already covered. so, in this example, her displacement is 0, because she went over the same length she already covered.  another way to look at this is by using a boomerang as an example. if you throw a boomerang, it will always come back to you. suppose you threw it & it travelled 10 feet then came back. it is said to have travelled 20 feet (10 one way & 10 on the way back) but to have a displacement of 0 because, relative to its starting position & its destination, it returned to the starting point & so it isn't considered to have shifted its position. the distance it travells is irrelevant.  another way to look at it is if you go on a trip, say a 1-day fishing trip. suppose you go to a lake that's 100 miles from where you live. you go there, you stop, you fish & do whatever, then return home. you travelled a total of 200 miles in that day. but, does that mean that just because you travelled those 200 miles then you moved & you now live in a different home at a different address? of course not.  but, if you stopped for gas on the way, then your displacement equals the extra distance you travelled to get to the gas station.  so, onto your questions:  2.    jack and jill set out for a morning run. they both run 2 miles north along rte 3 and then turn and run back south to home (to the starting point). jill stops at home, but jack continues to run south for an additional 3 miles to the gym.  a. how far did jill run? (remember the definition of distance.)  jill ran 4 miles.  b. what was the displacement for her entire run? (remember the definition of displacement.)  her displacement for her entire run was 0.  c. how far did jack run? (remember the definition of distance.)  jack ran 7 miles.  d. what was the displacement for his entire run? (remember the definition of displacement.)  his displacement for his entire run was 3 miles, the distance from the starting point (home) to the gym.  i hope that helped.