The problem can be solved using the formula for acceleration:

$a = \frac{v_f - v_i}{t}$

Where:

• $v_i$ = initial velocity = $90 \, \text{km/h}$,
• $v_f$ = final velocity = $0 \, \text{km/h}$,
• $t$ = time = $5 \, \text{s}$.

Step 1: Convert initial velocity to $\text{km/h}$ to $\text{m/s}$

$v_i = 90 \, \text{km/h} \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = 25 \, \text{m/s}$

Step 2: Apply the acceleration formula

$a = \frac{v_f - v_i}{t} = \frac{0 - 25}{5} = -5 \, \text{m/s}^2$

The negative sign indicates deceleration.

Step 3: Convert the result back to $\text{km/h}^2$

1 $\text{m/s}^2 = 12960 \, \text{km/h}^2$, so: $a = -5 \, \text{m/s}^2 \times 12960 = -64800 \, \text{km/h}^2$

Final Answer:

The deceleration is: $\boxed{-64800 \, \text{km/h}^2}$

Would you like a more detailed explanation or assistance with another part of the problem?

Here are 5 related questions for further exploration:

1. How can you calculate the distance traveled during the deceleration?
2. What is the significance of the negative sign in the acceleration value?
3. How would the calculation change if the bus took 10 seconds to stop?
4. How do you determine the stopping force acting on the bus if its mass is known?
5. What are the effects of different units (e.g., $m/s^2$ vs. $km/h^2$) on interpreting acceleration?

Tip: Always convert all quantities to consistent units (e.g., SI units) to avoid calculation errors.