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Standard IX

Physics

Time and Speed

Explain clear...

Question

Explain clearly, with examples, the distinction between:

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].

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Solution

Average speed and average velocity.
As path length is greater than or equal to the displacement, so average speed is also greater than the magnitude of average velocity. And the two quantities will be equal if the particle continues to move along a straight line, without changing the direction.

Final Answer:
Average Speed will be always greater than or equal to the magnitude of the average velocity.

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Similar questions

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].

(i)

Explain clearly, with examples, the distinction between :

(a) magnitude of displacement 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.

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 ?

(i i)

A man walks on a straight road from his home to a market

2.5 k m

away with a speed of

5 k m h^{- 1}

. Finding the market closed, he instantly turns and walks back home with a speed of

7.5 k m h^{- 1}

. What is the:
(a) magnitude of average velocity, and
(b) average speed of the man over the interval of time (i)

0

30 m i n

, (ii)

0

50 m i n

, (iii)

0

40 m i n

Read each statement below carefully and state with reasons, if it is true or false:

(a) The magnitude of a vector is always a scalar, (b) each component of a vector is always a scalar, (c) the total path length is always equal to the magnitude of the displacement vector of a particle. (d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector.

Q. If magnitude of average speed and average velocity over a time interval are same, then

Q. Which of the following statements are incorrect?
(i) Average velocity is path length divided by time interval.
(ii) In general, average speed is greater than the magnitude of the average velocity.
(iii) A particle moving in a given direction with a non-zero velocity can have zero speed.
(iv) The magnitude of average velocity is the average speed.

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Time and Speed

Standard IX Physics

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Explain clearly, with examples, the distinction between: 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].

Explain clearly, with examples, the distinction between:

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].