1. **State the problem:** A child slides down a playground slide starting from rest and reaches a speed of 4.5 m/s at the end of the slide, which is 2.8 m long. We need to find the acceleration experienced by the child. 2. **Identify known values:** - Initial velocity, $v_0 = 0$ m/s (starting from rest) - Final velocity, $v = 4.5$ m/s - Displacement, $s = 2.8$ m 3. **Formula used:** We use the kinematic equation that relates velocity, acceleration, and displacement without time: $$v^2 = v_0^2 + 2as$$ where $a$ is acceleration. 4. **Rearrange the formula to solve for acceleration $a$:** $$a = \frac{v^2 - v_0^2}{2s}$$ 5. **Substitute the known values:** $$a = \frac{(4.5)^2 - (0)^2}{2 \times 2.8}$$ 6. **Calculate numerator and denominator:** $$a = \frac{20.25 - 0}{5.6}$$ 7. **Simplify the fraction:** $$a = \frac{20.25}{5.6}$$ 8. **Perform the division:** $$a \approx 3.6161$$ 9. **Round to two decimal places:** $$a \approx 3.62$$ **Final answer:** The acceleration experienced by the child is approximately $3.62$ m/s$^2$.