given u = 5 and and v = 15 m/s and t=7.5 hat is s

To find the displacement \( s \) given the initial velocity \( u \), final velocity \( v \), and time \( t \), you can use the following SUVAT equation:

\[
s = \frac{(u + v)}{2} \times t
\]

This equation is derived from the definition of average velocity:

\[
\text{Average velocity} = \frac{u + v}{2}
\]

### Step 1: Substitute the given values into the equation:

\[
u = 5 \text{ m/s}, \quad v = 15 \text{ m/s}, \quad t = 7.5 \text{ seconds}
\]

\[
s = \frac{(5 + 15)}{2} \times 7.5
\]

### Step 2: Calculate the displacement \( s \):

\[
s = \frac{20}{2} \times 7.5 = 10 \times 7.5 = 75 \text{ meters}
\]

### Final Result:
- **Displacement, \( s = 75 \text{ meters} \)**

Do you want details or have any questions? Here are five related questions to expand your understanding:

1. How would the displacement change if the initial velocity was doubled?
2. Can you find the acceleration using the same values for \( u \), \( v \), and \( t \)?
3. What if the time was reduced to 5 seconds? What would be the new displacement?
4. How does this method compare to using the equation \( s = ut + \frac{1}{2}at^2 \)?
5. How would the displacement change if both \( u \) and \( v \) were reduced by half?

**Tip:** The average velocity method is quick and effective when both initial and final velocities are known.

Learn how to calculate displacement using initial velocity, final velocity, and time with a step-by-step explanation. This problem involves using the average velocity formula to find displacement in physics. Suitable for Grades 9-12.

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