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Distance And Displacement - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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33 Questions around this concept.
Solve by difficulty
Calculate the path length of a semicircular path having a radius $r$
Assertion: For unidirectional movement of an object, displacement > distance.
Reason: For unidirectional movement of an object, displacement = distance.
A particle moves from A to C by path ABC is shown in the given diagram. The displacement of the particle is
6 m
Which of the following statement is true for displacement of a moving object?
A container is kept in a moving bus.
A particle is moving along north after moving for 2 sec with a speed of 4 m/s, its speed becomes 5m/s.What is its displacement (in meters) at end of 7 sec
Direction: In the following question, a statement of Assertion (A) is followed by a statement of reason (R). Mark the correct choice as :
Assertion: displacement of the particle is the shortest distance between the initial and final position but distance is the actual length of the path
Reason: Displacement is the vector quantity but distance is a vector quantity
If the displacement of a particle is zero, distance covered :
The position vector of a particle is $\vec{r}=2 t^2 \hat{i}+3 t \hat{j}+4 \hat{k}$
Then the displacement of the particle in time interval $t=0$ to $t=1 \mathrm{~s}$
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Concepts Covered - 1
Distance and displacement
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Position vector
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The position of a point, in space, is an important physical quantity which is also known as position vectors.
- Representation of position vector $\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$
- Its magnitude is the distance between the initial point (tail) and the final point (head).Jenerally, we take initial point as origin)
- Its direction is from the initial point and the final point.Magnitude of $r=\sqrt{x^2+y^2+z^2}$
- E.g. If $\vec{A}=3 \hat{i}-4 \hat{j}+2 \hat{k}$ then its magnitude$$
\begin{aligned}
& =\sqrt{(3)^2+(-4)^2+(2)^2} \\
& =\sqrt{9+16+4} \\
& a=\sqrt{29}
\end{aligned}
$$2. Distance or Path length
- Length of the actual path between the initial and final positions of the body.
- E.g. Distance travelled along a circle for one complete rotation is $2 \pi r$
- Tips of distance,,
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Distance is a scalar quantity.
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It is always positive.
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S.I. Unit: meter (m).
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Dimension [L]
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Distance is depend on the path followed by the body.
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Displacement
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The shortest path is between the initial and final positions.
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Tips for Displacement.
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Displacement is a vector quantity.
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It can be positive, zero or negative.
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Displacement is independent of path.
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S.I. unit: Meter (m)
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Dimension (L)
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The magnitude of Displacement $\leqslant$ Distance.
- E.g. For Semi circleDistance $=\pi r$ while Displacement $=2 r$
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