Calculation of distance travelled
and displacement
(from O to A through C )
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Answers
Answer:
Distance and displacement are two quantities that seem to mean the same but are distinctly different with different meanings and definitions. Distance is the measure of “how much ground an object has covered during its motion” while displacement refers to the measure of “how far out of place is an object.” In this article, let us understand the difference between distance and displacement.
What is Distance?
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
Let’s understand the concept of distance with the help of the following diagram:
Boy cycling his way back home from a reference point A crossing point C to get to point B
Explanation of distance
Distance here will be = 4m + 3m + 5m = 12 m
Distance Formula
\Delta d =d_{1} + d_{2}
How is Displacement defined?
Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position. For example- If an object moves from A position to B, then the object’s position changes. This change in position of an object is known as Displacement.
Distance And Displacement
Displacement = \Delta x = x_{f}- x_{0}
x_{f} = Final Position
x_{0} = Initial Position
\Delta x = Displacement
Explanation:
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Distance and Displacement – Definitions
The total path covered by a particle in a given interval of time is called the distance travelled by that particle.
Distance and displacement
Distance is a scalar quantity. For a moving body, the distance covered is always positive. The SI unit for distance is metre and its dimensional formula is [M0L1T0].
Consider a particle moving from P to R via Q as shown in figure 1.
Then, the distance covered = PQ + QR
Displacement may be defined as the change in position of a particle along a given direction.
The displacement is the shortest distance between the two points. It is obtained by drawing a straight line vector from initial to final positions. In figure 1,
\begin{aligned} \overrightarrow{PR} \end{aligned} is the displacement. It is a vector quanity and is represented by
\begin{aligned} \overrightarrow{PR} \end{aligned}. It can have any value i.e., a zero, –ve or +ve. If the particle is travelling from R to P along any path, the displacement is represented
\begin{aligned} \overrightarrow{RP} \end{aligned}. Then
\begin{aligned} \overrightarrow{RP} = -\overrightarrow{PR} \end{aligned}.
If the particle moves from P to R and then from R to P along any path, the net displacement
\begin{aligned} \overrightarrow{PR} + \overrightarrow{RP} = 0 \end{aligned}.
The unit and dimensions of displacement are the same as that for the distance which is metre and [ M0L1T0 ] respectively.
example
In the case of a body circulating around a circle of radius r, when it completes a semi-circle AB, the distance covered is πr, while displacement is 2r. When it completes one revolution, the distance covered is 2πr and the displacement is zero.
Consider an object projected vertically from the top of a building of height h. The object moves a distance l upwards and returns to the ground. Now the distance travelled is (2l + h) while the displacement is –h.
Features of displacement
Displacement is a vector quantity. It can be a positive,a negative or a zero value.
The magnitude of displacement of a particle between two points gives the shortest distance between the two points.
The SI unit for displacement is metre and it has the dimension of length [M0L1T0]
The magnitude of the displacement will be less than or equal to the actual distance travelled by the object in the given interval of time.
i.e., |Displacement| ≤ Distance
If an object, after travelling a certain distance returns to the starting point, then its displacement is zero.
The displacement of the object between two points has a unique value.
The displacement of an object is unaltered due to a shift in the origin of the position axis.
The numerical ratio of displacement to distance is equal to or less than one.
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