A truck's velocity on a highway increases uniformly from 20km/hr to 75km/hr in 30 seconds. Determine the average speed in m/s

To determine the average speed of the truck in meters per second (m/s), we'll follow these steps:

### Step 1: Convert the velocities from km/h to m/s.
- The initial velocity \(v_i = 20\) km/h.
- The final velocity \(v_f = 75\) km/h.

The conversion factor from km/h to m/s is \( \frac{5}{18} \).

So:
\[
v_i = 20 \times \frac{5}{18} = \frac{100}{18} \approx 5.56 \, \text{m/s}
\]
\[
v_f = 75 \times \frac{5}{18} = \frac{375}{18} \approx 20.83 \, \text{m/s}
\]

### Step 2: Calculate the average speed.
For uniformly increasing velocity, the average speed \( v_{avg} \) is given by the formula:
\[
v_{avg} = \frac{v_i + v_f}{2}
\]

Substituting the values:
\[
v_{avg} = \frac{5.56 + 20.83}{2} \approx \frac{26.39}{2} \approx 13.195 \, \text{m/s}
\]

### Answer:
The average speed of the truck is approximately **13.195 m/s**.

Would you like any more details or explanations on how this is calculated?

Here are some related questions:

1. How do you calculate average velocity in cases of non-uniform acceleration?
2. What is the difference between average speed and average velocity?
3. How do you convert from m/s back to km/h?
4. How would the average speed change if the truck accelerated non-uniformly?
5. Can you find the total distance traveled by the truck during these 30 seconds?
6. What is the significance of average speed in real-world driving scenarios?
7. How does this calculation differ when considering different units (e.g., miles per hour)?
8. How would the result change if the time duration was different?

**Tip:** Always ensure you're using consistent units when calculating speed or velocity to avoid errors.

Learn how to calculate the average speed of a truck that uniformly increases its velocity from 20 km/h to 75 km/h in 30 seconds. Step-by-step solution with unit conversion and formula application provided.

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