Question

The ADCL IIT Foundation conference theatre of a school is 15 m wide and has a door at a corner. A teacher enters at 8.00 am through the door and makes 10 rounds along the 15 m wall back and forth during the period and finally leaves the class-room at 9.30 a.m. through the same door. What will be his average speed and average velocity?

Answer 1

Given:

The ADCL IIT Foundation conference theatre of a school is 15 m wide and has a door at a corner.

A teacher enters at 8.00 am through the door and makes 10 rounds along the 15 m wall back and forth during the period and finally leaves the class-room at 9.30 a.m. through the same door.

To find:

What will be his average speed and average velocity?

Solution:

IIT Foundation School width = 15m,

The number rounds made by a teacher along the width 15m = 10 the time period for the above duration = 9.30 - 8.00 = 90 min.

Average speed = total distance travelled / Total time taken

= (15 × 10) / 90 = 5/3 m/min

As the teacher made even rounds, his final position is equal to the initial position. Hence displacement of a teacher is zero.

Therefore, the average velocity of a teacher is zero.

Answer 2

Given that,

Width of door = 15 m

Time of enters = 8: 00 am

Number of round = 10

Length of well = 15 m

According to question,

The total time is

$T=9:30-8:00$

$T=30\ min$

The total distance is

$D = 10\times15$

$D=150\ m$

We need to calculate the average speed

Using formula of average speed

$average\ speed=\dfrac{D}{T}$

Where, D = total distance

T = total time

Put the value into the formula

$average\ speed=\dfrac{150}{30\times60}$

$average\ speed =0.0833\ m/s$

A teacher enters through the door and makes 10 rounds along the 15 m wall back and forth during the period and finally leaves the classroom.

The final position of teacher equal to the initial position of the teacher.

So, the displacement is zero.

We need to calculate the average velocity

Using formula of average speed

$average\ velocity=\dfrac{D}{T}$

Where, D = total displacement

T = total time

Put the value into the formula

$average\ velocity=\dfrac{0}{30\times60}$

$average\ velocity = 0$

Hence, (I). The average speed of the teacher is 0.0833 m/s.

(II). The average velocity of the teacher is zero.