Question

Two persons X and Y take $10hours$ and $12hours$ respectively to travel from Bangalore to Hyderabad, then the

• A. average velocity of X is equal to the average velocity of Y.
• B. average velocity of X is less than that of Y.
• C. average velocity of X is more than that of Y.
• D. We cannot compare their velocities.

Answer 1

The correct option is C

average velocity of X is more than that of Y.

Velocity:

1. The rate of change of displacement is defined as velocity.
2. $v=\frac{displacement}{time}=\frac{s}{t}$
3. It is in terms of $m{s}^{-1}$

Average velocity:

1. Average velocity is defined as the total displacement of an object over a period of time
2. $v_{average}=\frac{totaldisplacement}{totaltime}$
3. It is in terms of $m{s}^{-1}$

Explanation for the correct option:

Option C:

1. X takes $10hours$ to travel from Bangalore to Hyderabad whereas Y takes $12hours$for the same journey.
2. As X is traveling faster than Y, the average velocity of X must be higher than the average velocity of Y.

Explanation for the incorrect options:

Option A:

1. If the average velocity of X is equal to the average velocity of Y, then they must have covered the equal distance in equal time.
2. As Y is taking more time than X, it cannot be true.

Option B:

1. If the average velocity of X is less than that of Y then Y must have taken less time.
2. But as Y has taken two hours more than X to cover the same distance, it cannot be true.

Option D:

1. We can compare their velocities as the time for the whole journey is given.
2. Velocity is calculated for the distance covered in a particular time.
3. Average velocity is calculated when total distance and total time are given.
4. Hence, option d is the incorrect option.

Hence, option C is the correct option.