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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

  • 32 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

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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

 

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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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In the following cases, mark the correct answer(s):

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).

    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,,

  1. Distance is a scalar quantity.

  2. It is always positive.

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

  4. Dimension [L]

  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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