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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

  • 13 Questions around this concept.

Solve by difficulty

Assertion: For unidirectional movement of an object, displacement > distance.

Reason: For unidirectional movement of an object, displacement = distance.

 

Concepts Covered - 1

Distance and displacement
  1. Position vector

  • 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). 

(Generally, 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 

= \sqrt{(3)^{2}+(-4)^{2}+(2)^{2}}

= \sqrt{9+16+4}

a= \sqrt{29}

 

  1. 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

  1. Distance is a scalar quantity.

  2. It is always positive.

  3. S.I. Unit: meter (m).

  4. Dimension \left [ L \right ]

  5. Distance is depend on the path followed by the body.  

 

  1. Displacement

  • The shortest path is between the initial and final positions.

  • Tips for Displacement.

  1. Displacement is a vector quantity.

  2. It can be positive, zero or negative.

  3. Displacement is independent of path.

  4.  S.I. unit:  Meter (m)

  5. Dimension  (L)

  6. The magnitude of Displacement \leqslant Distance. 

  •   E.g. For Semi circle

     Distance=\pi r  while Displacement =2\, r

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Distance and displacement

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