A bus changes its velocity from 10 km/h to 50 km/h. In how many seconds it did do it if the bus accelerates at a rate of 3.3 m/s²?

To determine the time it takes for the bus to change its velocity, we can use the formula for acceleration:

\[
a = \frac{v_f - v_i}{t}
\]

Where:
- \( a \) is the acceleration (3.3 m/s²),
- \( v_f \) is the final velocity (50 km/h),
- \( v_i \) is the initial velocity (10 km/h),
- \( t \) is the time in seconds.

First, we need to convert the velocities from km/h to m/s:

\[
v_f = 50 \, \text{km/h} = \frac{50 \times 1000}{3600} \, \text{m/s} = 13.89 \, \text{m/s}
\]

\[
v_i = 10 \, \text{km/h} = \frac{10 \times 1000}{3600} \, \text{m/s} = 2.78 \, \text{m/s}
\]

Now, plug the values into the formula and solve for \( t \):

\[
3.3 = \frac{13.89 - 2.78}{t}
\]

\[
3.3 = \frac{11.11}{t}
\]

\[
t = \frac{11.11}{3.3} \approx 3.37 \, \text{seconds}
\]

So, the bus took approximately 3.37 seconds to change its velocity from 10 km/h to 50 km/h.

Would you like a more detailed explanation, or do you have any further questions?

Here are 5 related questions for you:
1. How do you convert between m/s and km/h?
2. What is the significance of the acceleration value in this context?
3. How would the time change if the acceleration were different?
4. Can you calculate the distance covered during this acceleration?
5. How would you find the final velocity if the time and acceleration were given?

**Tip:** Always double-check unit conversions when solving physics problems, as mismatched units can lead to incorrect results.

Learn how to calculate the time it takes for a bus to change velocity from 10 km/h to 50 km/h using an acceleration of 3.3 m/s². Includes step-by-step solution with unit conversions and formula application.

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