To determine the average speed between 10 seconds and 30 seconds, we need to follow these steps:
1. Identify the Initial and Final Speeds:
- The speed at 10 seconds is given as 10 m/s.
- The speed at 30 seconds is given as 40 m/s.
2. Calculate the Average Speed:
- The formula to calculate the average speed when the speeds at two different times are known is:
[tex]\[
\text{Average Speed} = \frac{\text{Initial Speed} + \text{Final Speed}}{2}
\][/tex]
3. Substitute the Given Values into the Formula:
- Initial Speed = 10 m/s
- Final Speed = 40 m/s
So we have:
[tex]\[
\text{Average Speed} = \frac{10 \, \text{m/s} + 40 \, \text{m/s}}{2}
\][/tex]
4. Perform the Calculation:
- Add the initial and final speeds first:
[tex]\[
10 \, \text{m/s} + 40 \, \text{m/s} = 50 \, \text{m/s}
\][/tex]
- Then divide the sum by 2:
[tex]\[
\frac{50 \, \text{m/s}}{2} = 25 \, \text{m/s}
\][/tex]
Therefore, the average speed from 10 seconds to 30 seconds is [tex]\( \boxed{25 \, \text{m/s}} \)[/tex].
