You are racing an Artificially Intelligent Robot, called Al, that you built. You can run at a constant speed of $10$ m/s throughout the race. Meanwhile, Al starts running at a constant speed of $ 1$ m/s. Thereafter, when exactly $ 1$ second has passed from when Al last changed its speed, Al’s speed instantaneously becomes $1$ m/s faster, so that Al runs at a constant speed of $k$ m/s in the kth second of the race. (Start counting seconds at $ 1$). Suppose Al beats you by exactly $1$ second. How many meters was the race?
1. Let's denote the length of the race by \( d \) meters.
2. You run at a constant speed of \( 10 \) m/s, so the time it takes for you to complete the race is \( \frac{d}{10} \) seconds.
3. Al's speed increases by \( 1 \) m/s every second. In the \( k \)-th second, Al runs at \( k \) m/s.
4. The distance Al covers in the \( k \)-th second is \( k \) meters.
5. The total distance Al covers in \( t \) seconds is the sum of the first \( t \) positive integers:
   \[
   \text{Distance covered by Al} = 1 + 2 + 3 + \cdots + t = \frac{t(t+1)}{2}
   \]
6. According to the problem, Al beats you by exactly \( 1 \) second. Therefore, if you take \( t \) seconds to complete the race, Al takes \( t-1 \) seconds.
7. The distance you cover in \( t \) seconds is:
   \[
   d = 10t
   \]
8. The distance Al covers in \( t-1 \) seconds is:
   \[
   d = \frac{(t-1)t}{2}
   \]
9. Since both distances are equal, we set up the equation:
   \[
   10t = \frac{(t-1)t}{2}
   \]
10. Multiply both sides by \( 2 \) to clear the fraction:
    \[
    20t = t^2 - t
    \]
11. Rearrange the equation to form a quadratic equation:
    \[
    t^2 - 21t = 0
    \]
12. Factor the quadratic equation:
    \[
    t(t - 21) = 0
    \]
13. Solve for \( t \):
    \[
    t = 0 \quad \text{or} \quad t = 21
    \]
14. Since \( t = 0 \) is not a valid solution in this context, we have:
    \[
    t = 21
    \]
15. The length of the race is:
    \[
    d = 10t = 10 \times 21 = 210 \text{ meters}
    \]

The final answer is \( \boxed{210} \) meters.