Distance and displacement are two quantities that seem to mean the same but are distinctly different with different meanings and definition. 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 with the following diagram
Distance here will be = 4m + 3m + 5m = 12 m
Distance Formula
\(\Delta d =d_{1} + d_{2}\)
How is Displacement defined?
Displacement = \(\Delta x = x_{f}- x_{0}\)
\(x_{f}\) = Final Position
\(x_{0}\) = Initial Position
\(\Delta x\) = Displacement
Examples ofÂ Distance And Displacement
Question 1. John travels 250 miles to North but then back-tracks to South for 105 miles to pick up a friend. What is Johnâ€™s total displacement?Â
Answer: Johnâ€™s starting positionÂ Xi= 0.
Her final position Xf is the distance travelled N minus the distance South.
Calculating displacement, i.e.D.
D = Î”X = (Xf – Xi)
D = (250 mi N – 105 mi S) – 0
D = 145 mi N
Question 2. Julia throws the ball 30 feet North for your dog. The dog catches the ball and takes it past Julia to her brother, who is standing 5 feet to the South of where she is. Calculate the total displacement of the ball?
Answer: Juliaâ€™s initial position with the ball ( Xi) = 0.
As displacement is a vector quantity, ‘direction’ is considered. Xf = (30 feet S – 25 feet N),
so, Xf = -5 feet S.
D = Î”X = (Xf – Xi)
D = (30 ft S – 25 ft S) – 0
D = 5 ft S of Julia’s starting position
Distance vs Displacement
Distance |
Displacement |
The complete length of the path between any two points is called distance |
Displacement is the direct length between any two points when measured along the minimum path between them |
Distance is a scalar quantity as it only depends upon the magnitude and not the direction |
Displacement is a vector quantity as it depends upon both magnitude and direction |
Distance can only have positive values |
Displacement can be positive, negative and even zero |
Read More: Difference Between Distance and Displacement
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