Distance, Displacement, Speed and Velocity
Distance: The path length covered by the body is called distance.it is a scalar quantity.
Units: cm (In C.G.S. System); m(In S.I. System)
Displacement: The shortest pathlength between the initial and final positions of a body iscalled displacement. It is a vector quantity.
Units: cm (In C.G.S. System); m(In S.I. System)
Examples:
1) Suppose a bus starting from station A travels 15000 m to reach stationB then the distance covered by the bus is 15000 m. Now if the bus returns to the station A then distance covered is 15000 m and the total distance covered by the bus during the trip from A to B and then back to A from B is 15000 m + 15000 m = 30000 m.
But the displacement when the bus moves from A to B and then from B to A is zero
2) Suppose a person moves 3 meters from A to B and 4 meters from B to C as shown in the figure. The total distance traveled by him is 7 meters and he is displaced only by 5 m which is the shortest distance between his initial position and final position.
Ex:Now let us consider an object changing its position, with respect to a fixed point called the origin 0. xi and xf are the initial position and final position of the object. Then the displacement of the object = xf – xi
Case 1
Suppose the object is moving from +1 to +4, then displacement = xf – xi = +4 – (+1) = +3
Case 2
If the object is moving from -3 to -1 then displacement = xf – xi = –1 – (–3)= 2
Case 3
If the object is moving from +5 to +2 then displacement = xf – xi = +2 – (+5) = –3.
Case 4
If the object follows the path as shown in the figure then the final position and the initialposition is the same i.e., the displacement is zero.
Example:An athlete completes one round of a circular track of radius R in 40 s. What will be his displacement at the end of 2 min 20 s?
Sol. The time = 2 min 20s = 140s
In 40 seconds athlete completes = 1 round
In 140 seconds athlete will completes
\(\frac{{140}}{{40}}\)round =3.5 rounds
The displacement in 3 rounds = 0
So net displacement =2R
Getting Direction:On the Earth the directions parallel to the ground which are North, East,West & south directions are horizontal and
they are represented on paper as in side figure.
The direction exactlly midway between N and E is called NE.
Similarly NW, SW & SE.