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The question asks to find the initial speed of a bus. Here’s how we can solve it:

### Given:
- Initial speed of the bus = \( v_0 \) km/h (we need to find this).
- The speed increases by 9 km/h every hour.
- The bus travels 572 km in 11 hours.

### Concept:
The bus is accelerating at a uniform rate, so its speed at each hour is increasing. This is similar to an arithmetic progression, where:
- The first term is \( v_0 \),
- The common difference is 9 km/h,
- The total time is 11 hours,
- The total distance is 572 km.

### Formula:
The total distance traveled under uniform acceleration is given by the sum of an arithmetic progression (AP):
\[
S = n \times \frac{v_0 + v_n}{2}
\]
where:
- \( S \) is the total distance (572 km),
- \( n \) is the time (11 hours),
- \( v_n \) is the speed at the end of 11 hours.

The final speed \( v_n \) after 11 hours will be:
\[
v_n = v_0 + (n-1) \times 9 = v_0 + 10 \times 9 = v_0 + 90
\]

Substitute \( v_n \) and solve for \( v_0 \):
\[
572 = 11 \times \frac{v_0 + (v_0 + 90)}{2}
\]
\[
572 = 11 \times \frac{2v_0 + 90}{2}
\]
\[
572 = 11 \times (v_0 + 45)
\]
\[
572 = 11v_0 + 495
\]
\[
11v_0 = 572 - 495 = 77
\]
\[
v_0 = \frac{77}{11} = 7 \, \text{km/h}
\]

### Answer:
The initial speed of the bus is **7 km/h**.

Would

A bus starts running with some initial speed and its speed increases every hour by 9 km/hr. If it takes 11 hours to cover a distance of 572 km, then what was the initial speed (in km/hr) of the bus?

Learn how to calculate the initial speed of a bus where the speed increases by 9 km/hr every hour. This problem involves arithmetic progression, algebra, and speed-time-distance concepts. Suitable for students in Grades 9-11.

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