NCERT Class 11 Physics Solutions: Chapter 3 – Motion in a Straight Line Part 7

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Question: 3.13

Explain clearly, with examples, the distinction between:

a) Magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;

b) Magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first.

When is the equality sign true? [For simplicity, consider one-dimensional motion only].

Answer:

a)

  • The magnitude of displacement over an interval of time is the shortest distance (which is a straight line) between the initial and final positions of the particle.

  • The total path length of a particle is the actual path length covered by the particle in a given interval of time.

  • For example, suppose a particle moves from point A to point B and then, comes back to a point, C taking a total time t, as shown below. Then, the magnitude of displacement of the particle

Image shows the AB line

Image Shows the AB Line

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  • Whereas, total path length

  • It is also important to note that the magnitude of displacement can never be greater than the total path length. However, in some cases, both quantities are equal to each other.

b)

  • Magnitude of average velocity

  • For the given particle,

  • Average velocity

  • Average speed

  • Since average speed is greater than the magnitude of average velocity.

  • The two quantities will be equal if the particle continues to move along a straight line.

Equations of Average speed and velocity for 2nd ques

Equations of Average Speed and Velocity for 2nd Ques

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Question 3.14:

A man walks on a straight road from his home to a market away with a speed of. Finding the market closed, he instantly turns and walks back home with a speed of. What is the

a) Magnitude of average velocity, and

b) Average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min?

[Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speeds was zero!]

Answer:

Equations of Average speed and velocity

Equations of Average Speed and Velocity

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  • Time taken by the man to reach the market from home

  • Time taken by the man to reach home from the market,

  • Total time taken in the whole journey

  • Average velocity

  • Average speed

  • Time

  • Net displacement

  • Total distance

  • Average velocity

  • Average speed

  • Speed of the man

  • Distance travelled in first

  • Distance travelled by the man (from market to home) in the next 10 min

  • Net displacement

  • Total distance travelled

  • Average velocity

  • Average speed