When we move from one place to another,
the measure of total length we cover
is called the distance.
So you have to travel to this town
and the best route is straight up north.
But because of road works along the way,
we have to take a detour,
and the distance covered would be something like this.
Now when the road works are completed,
the distance needed to be covered
would be something like this.
Distance is measured in meters
and denoted as a lower case "m".
The distance between these two towns
is about twenty thousand meters,
but because of the detour,
you had to cover a distance of fifty thousand meters.
Okay,
so nobody likes big numbers,
unless it’s your salary.
So we should also know
that a kilometer is one thousand meters.
In our example,
we can say that instead of 20 kilometers,
you travelled 50 kilometers.
Is distance a scalar or a vector quantity?
Think about it...
If you say someone travelled 20kms from this point,
we can't really tell where they landed up.
Maybe here,
maybe there,
or maybe they just went around in circles.
As it does NOT specify a direction,
it is a SCALAR quantity.
That brings us to Displacement.
So what is displacement?
“Distance with DIRECTION” is displacement.
Distance with direction?
What do we mean by that?
You made two separate trips to this town.
Was the distance covered in both the cases the same?
Have a good look.
It wasn’t.
In each of the two cases the distance was different.
The time you took for the detour
was greater than the time you could go straight across.
But if you call someone to tell them where you are,
in both the cases your location is this town,
which is 20kms north of your home.
The displacement in both the cases is the same.
You travelled 20 kms north.
North shows the direction
and because direction is specified,
displacement becomes a VECTOR QUANTITY.
Look at this example where a mother asks her son
to quietly stay where he is while she takes a quick nap...
so now the child runs back and forth many times and
returns to the original spot before the mum wakes up.
Mum wakes up and sees the child in the same spot
and as she hasn’t observed
what happened in the last few minutes,
she assumes the child has not moved.
The child,
being the future expert in physics,
has in fact disobeyed her instruction
and covered lots of distance…
but at the same time
he can argue that he did follow his mum’s instruction.
Lots of distance covered but ZERO displacement!
If the distance travelled is a straight line,
the displacement will be the same magnitude
as the distance but with the direction provided as well.
In MOST cases in our day to day lives,
the distance covered
is greater than the displacement seen.
Running errands and travelling back
and forth between places
cause the amount of distance to build up,
though you may not end up very far from home.
If you’ve really understood the
difference between distance and displacement,
you should be able to answer the next question.
When a passenger travels by taxi,
is he charged based on the distance
or displacement?
Taxis charge passengers based on DISTANCE.
If you go to the neighboring town
and return in the same taxi,
the taxi meter shows you the charge for the
entire round trip.
If you now try to explain to the taxi driver
that you have had no resultant change in your location,
and hence you must pay nothing,
it will not impress him much.
