Motion In A Straight Line
Distance and displacement are concepts used to describe the motion of an object in physics. While they both refer to the location change of an object, they have distinct meanings and are measured differently.
Distance:
Distance is a scalar quantity that represents the total path length traveled by an object. It is a measure of the actual physical length of the path taken by the object and is always non-negative.
Distance is a scalar because it only has magnitude and no direction associated with it.
The SI unit of distance is the meter (m).
Displacement:
Displacement is a vector quantity that represents the change in position of an object. It is the straight-line distance and direction from the initial position to the final position.
Displacement considers the overall change in position, regardless of the path taken, and includes both magnitude and direction.
Displacement can be zero even if the distance traveled is not zero. For example, if an object moves in a closed loop and returns to its initial position, the displacement is zero.
The SI unit of displacement is also the meter (m), but it is a vector quantity and is typically expressed with both magnitude and direction.
To illustrate the difference between distance and displacement, consider the following example:shown in the figure.
Ex: An athlete covers 3 rounds on a circular track of radius 50 m. Calculate the total distance and displacement travelled by him.
Solution:
The total distance the athlete covered =3x circumference of track
=3x2\( \pi \)r
=6x3.14x50
=942m
The displacement is zero, since the athlete reaches the same point A after three rounds from where he started.
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:A person walks 4 meters east, then walks 3 meters north. Determine distance and displacement.
ex:Suppose an object moves in a straight line along a coordinate axis. The object starts at point A and moves to point B.
Initial position (A): xi=0 m
Final position (B): xf=10 m
Now, let's calculate the distance traveled and displacement.
Calculations:
Distance (d):
d=|xf-xi|
d=|10 m-0 m|=10 m
Displacement :
x=xf-xi
x=10 m-0 m=10m.
Speed and velocity are both measures of how fast an object is moving, but they have distinct definitions and characteristics.