1. **State the problem:** A car starts from rest (initial velocity $u=0$) and accelerates uniformly to a final velocity $v=30$ m/s in $t=8$ seconds. We need to find the acceleration $a$ and the distance traveled $s$ in this time. 2. **Formulas used:** - Acceleration: $$a=\frac{v-u}{t}$$ - Distance traveled under uniform acceleration: $$s=ut+\frac{1}{2}at^2$$ 3. **Calculate acceleration:** Since $u=0$, $$a=\frac{30-0}{8}=\frac{30}{8}=3.75\text{ m/s}^2$$ 4. **Calculate distance traveled:** Using $s=0 \times 8 + \frac{1}{2} \times 3.75 \times 8^2$ $$s=\frac{1}{2} \times 3.75 \times 64=1.875 \times 64=120\text{ meters}$$ 5. **Answer:** The acceleration is $3.75$ m/s$^2$ and the car travels $120$ meters in 8 seconds.