When you go to school, you cover some distance. Suppose there is a large lake in front of your house. Due to it, you have to take the long green path to reach your school.
By the time you reach the school, you cover a distance
equal to the length of the green road;
but your displacement is equal to
the length of the red line.
Distance is the space or ground covered by an object,
when it moves. It is the total path travelled by an object.
Displacement is the difference between the initial and final position
of an object that has moved; more specifically, it is the
shortest distance between the initial and the final position.
The direction of movement is always
involved in displacement. The magnitude of displacement
may be positive, negative or zero.
Let an object move
1 - from point A to B eastward by 50 units;
2 - then towards north to point C by 30 units further;
3 - then further towards south-west to initial point A.
So, total distance travelled by the object is
50+30+58.31 = 138.31
units.
How length of side AC = 58.31 units ?
Since in right-angled ▲ABC,
AC² = AB² + BC²
[Pythagorous theorem],
=> AC = √(AB² + BC²),
=> AC = √(50² + 30²),
=> AC = √3400,
∴ AC = 58.31 units.
After travelling a distance of 138.31 units,
the object has gained 0 displacement, or we should say
no displacement at the end.
This is because calculation of displacement
considers the initial and the final
position of an object.
We see that the object moved and covered some distance.
But the initial and the final position
of the object are the same,
so the displacement of the object is zero here.
Let us take another example.
An athelete begins to run through a circular path
having a radius of 300 meter. When she reaches her
initial position, the distance covered will be equal to the
circumference of the circular path (2πr).
But even though
she had made one complete revolution and travelled a distance of 2πr unit, no
displacement happened, as her final position is the same
as her initial position.
Distance: A to B is ½ of circumference
Distance = ½ × 2.π.r
= π.r
= 3.1416 × 300
≈ 942.48
Displacement: A to B is length of diameter AB
Displacement AB = 2 × r
= 2 × 300
= 600
After completion of half-circle, distance travelled from A to B is 942.48m., while displacement occured from A to B is 600m.(AB being the diameter)
Distance: A to A is the circumference
distance = 2 π r
= 2 × 3.1416 × 300
≈ 1885
Displacement: A to A [no displacement]
Initial and final positions are the same.
∴ Displacement from A to A = 0
After completion of full-circle, distance covered from A to A is 1885m., while displacement occured from A to A is 0.
✫ A scalar quantity has only one property, magnitude.
Distance is a scalar quantity, it has magnitude only.
Other scalar quantities are area, volume, time etc.
✫ A vector quantity has both magnitude and direction.
Displacement is a vector quantity, it has magnitude as well as direction.
Other vector quantities are force, momentum, acceleration, weight etc.
Distance is scalar, displacement is vector
✓ Distance is a scalar quantity, and it is always positive.
✓ Displacement is a vector quantity, it may be positive, negative or zero.
Distance is a scalar quantity; it has magnitude only, and no direction. On the other hand, displacement is a vector quantity; it has magnitude, as well as direction.
No displacement, no work
✓If displacement of an object is zero, then no work is done.
W.r.t. motion, direction of a moving object has much importance when
calculating displacement,
velocity
and
acceleration.
In physics,
Work = Force × Displacement
.
So, if displacement is zero, then work is also zero,
which means no work is done.
Understanding displacement is a requirement
prior to proper understanding of
velocity and acceleration.
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