The distance (s) travelled by a particle varies with time (t) as : (s) = 1.2 t$^2$ meter. The average speed during time interval 0 to 10 second is :

Question

Accepted Answer

To determine the average speed of the particle during the time interval from 0 to 10 seconds, we need to calculate the total distance traveled and divide it by the total time taken.

The distance $ s $ traveled by the particle is given by the equation:
$$ s(t) = 1.2t^2 $$

1. **Calculate the distance at $ t = 0 $:**
   $$ s(0) = 1.2 \times 0^2 = 0 \, \text{meters} $$

2. **Calculate the distance at $ t = 10 $:**
   $$ s(10) = 1.2 \times 10^2 = 1.2 \times 100 = 120 \, \text{meters} $$

3. **Calculate the total distance traveled:**
   The total distance traveled from $ t = 0 $ to $ t = 10 $ is:
   $$ s(10) - s(0) = 120 - 0 = 120 \, \text{meters} $$

4. **Calculate the average speed:**
   The average speed is the total distance traveled divided by the total time:
   $$ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{120 \, \text{meters}}{10 \, \text{seconds}} = 12 \, \text{m/s} $$

Therefore, the average speed during the time interval from 0 to 10 seconds is 12 m/s, which corresponds to Option 4.

**Explanation for why other options are incorrect:**

- **Option 1 (6 m/s):** This option is incorrect because it underestimates the average speed. The calculation clearly shows that the average speed is 12 m/s, not 6 m/s.

- **Option 2 (24 m/s):** This option is incorrect because it overestimates the average speed. The calculated average speed is 12 m/s, which is half of 24 m/s.

- **Option 3 (36 m/s):** This option is incorrect because it significantly overestimates the average speed. The correct average speed is 12 m/s, which is much lower than 36 m/s.

In conclusion, the correct average speed is 12 m/s, making Option 4 the correct choice.