A sledge of mass 14 kg slides over smooth ice at 2.6 m/s…

Step 1. Acceleration. $a = \dfrac{21\ \text{N}}{14\ \text{kg}} = 1.5\ \text{m/s}^2$.

Step 2. Final speed. $v = 2.6\ \text{m/s} + 1.5\ \text{m/s}^2 \times 5.0\ \text{s} = 10.1\ \text{m/s}$.

Step 3. Distance. $s = 2.6\ \text{m/s} \times 5.0\ \text{s} + \tfrac12 \times 1.5\ \text{m/s}^2 \times (5.0\ \text{s})^2 = 13\ \text{m} + 18.75\ \text{m} = 31.75\ \text{m}$.