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.