1. **State the problem:** A racing car decelerates uniformly from an initial velocity $u = 75$ m/s to a final velocity $v = 15$ m/s over a distance $s = 270$ m. We need to find the rate of deceleration $a$. 2. **Formula used:** For uniformly accelerated motion, the equation relating velocities, acceleration, and displacement is: $$v^2 = u^2 + 2as$$ where $a$ is acceleration (negative for deceleration). 3. **Rearrange the formula to solve for $a$:** $$a = \frac{v^2 - u^2}{2s}$$ 4. **Substitute the known values:** $$a = \frac{15^2 - 75^2}{2 \times 270}$$ 5. **Calculate the squares:** $$a = \frac{225 - 5625}{540}$$ 6. **Simplify the numerator:** $$a = \frac{-5400}{540}$$ 7. **Simplify the fraction by canceling common factors:** $$a = \frac{\cancel{-5400}}{\cancel{540}} = -10$$ 8. **Interpretation:** The negative sign indicates deceleration. So, the rate of deceleration is $10$ m/s$^2$. **Final answer:** The rate of deceleration of the racing car is $10$ m/s$^2$.