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DISTANCE,DISPLACEMENT,SPEED &VELOCITY
DISTANCE,DISPLACEMENT,SPEED &VELOCITY
Distance & Displacement:
Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definitions and meanings.
Distance is a scalar quantity that refers to “how much ground an object has covered” during its motion.
Displacement is a vector quantity that refers to “how far out of place an object is”; it is the object’s overall change in position.
Units of Distance & Displacement: meter is the S.I. units of distance & displacement.
In the figure:1, The distance is indicated by dotted lines from A to B. That is entire path travelled by the body to reach the destination ‘B’. That total path travelled by the body is called Distance. And if a straight line drawn from point A to Point B, then that is the possible way to reach point B in shortest path. That shortest path is called as Displacement.
Some more examples:
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
Distance & Displacement in different cases:
Case 1:
Motion in straight path:
Displacement is the shortest distance between two points, while distance is the length of the path travelled. Therefore, if the body takes the shortest path between two points, distance and displacement will be equal. Imagine it in this way: Between two points you can draw any line-curved, with turns, etc, but you can draw only one straight line connecting the points which will be of the shortest distance. If an object travels across the curved line, the distance is equal to the length of the curved line, while displacement is equal to the length of the straight line. In case the object travels in this straight line, distance will be equal to the length of this line, which is also equal to displacement.
When an object is moving in straight path, then distance & displacement can be measured in same way because entire path travelled by the object & shortest path travelled by the object is same, so distance is equals to displacement.
Special case:
Here, displacement can be negative in some cases. To understand this, we need to take a fixed reference point for the motion of a body.
Case 2:
Motion in curved path:
When an object is moving in curved path, then distance & displacement can never be measured in same way because entire path travelled by the object & shortest path travelled by the object can never be same, so distance is not equal to displacement.
Case 3:
Motion in circular path:
If a body is moving in circular path, then the body will have distance & displacement also. But the displacement will be zero if the body comes back to the same point
again in its path. In this giant wheel, there are 20 cabinssituated at different places & each cabin is fixes at 1m apart from each other. Then if the giant wheel started moving then, Cabin-1 starts moving from its position (Reference point), if it moves to next position, thendistance & displacement will not be same, because it is not moving in straight path. If the Cabin-1 again comes back to same reference point, thendisplacement can be considered as zero.
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.
If the directions don't fall exactly midway then they won't be represented as NE, NW, SE, SW & SE. They are represented as in the following example
ex:An object moves 15 meters east, then 20 meters west, and finally 25 meters east. What is the net displacement of the object?
The net displacement is the sum of the individual displacements, considering direction: 15 m-20 m+25 m=20 m east.
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
\(140 \over 40\)round =3.5 rounds
The displacement in 3 rounds = 0
So net displacement =2R