Let's analyze the given problem.

The problem states:

• A bus accelerates from an initial speed of $u \, \text{m/s}$ to $25 \, \text{m/s}$ in $12$ seconds.
• The acceleration is given as $1.75 \, \text{m/s}^2$.
• We need to calculate the initial speed $u$.

We can use the kinematic equation: $v = u + at$ where:

• $v$ is the final velocity, $25 \, \text{m/s}$,
• $u$ is the initial velocity, which we need to find,
• $a$ is the acceleration, $1.75 \, \text{m/s}^2$,
• $t$ is the time, $12$ seconds.

Plugging in the values: $25 = u + (1.75)(12)$

Simplifying this: $25 = u + 21$ $u = 25 - 21$ $u = 4 \, \text{m/s}$

Answer:

The initial speed $u$ is $4 \, \text{m/s}$.

Would you like further explanation or have any other questions?

Here are five additional questions related to this topic:

1. How would the initial speed change if the acceleration was higher?
2. What formula would you use if you were given distance instead of time?
3. How do you calculate distance traveled with a constant acceleration?
4. What if the final velocity was unknown; how would you solve for $u$?
5. How does the time taken affect the initial speed if acceleration and final velocity are constant?

Tip: Always remember to check units in kinematic equations to ensure they are consistent throughout the calculation.