After 35 minutes of running, at the 8-{\rm km} point in a 9-{\rm km} race, you find yourself 200m behind the leader and moving at the same speed.

What should your acceleration be if you are to catch up by the finish line? Assume that the leader maintains a constant speed throughout the entire race.

To determine the required acceleration to catch up to the leader by the finish line, we need to analyze the situation using the kinematic equations of motion.

First, let's define our known values:
- Time: t = 35 minutes = 35 minutes * (1 hour / 60 minutes) = 35/60 hours = 7/12 hours.
- Distance of the race: d = 9 km.
- Distance at which you currently are: x = 8 km.
- Distance behind the leader: Δx = 200 m = 0.2 km.

Now, let's start by finding the speed at which the leader is moving.
Using the formula: Speed = Distance / Time, we can calculate the leader's speed:
Leader's Speed = d / t = 9 km / (7/12) hours = (9 * 12) / 7 = 108/7 km/h.

Since you are moving at the same speed as the leader, your current speed is also 108/7 km/h.

To determine the required acceleration, let's analyze the situation using the equation of motion:
Final Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Distance.

Let's assume the final velocity is the same for both you and the leader at the finish line, denoted as vf.

For the leader:
Initial Velocity = Leader's Speed = 108/7 km/h.
Distance = d - x = 9 km - 8 km = 1 km.

For you:
Initial Velocity = 108/7 km/h.
Distance = x - 0 km (since you are starting from the beginning).

Now, let's plug in the values into the equation and solve for the acceleration:

(108/7)^2 = (108/7)^2 + 2 * a * 1
0 = 2 * a * 1
a = 0.

From the above calculation, we can see that the required acceleration for you to catch up to the leader by the finish line is zero. This means you need to maintain a constant speed throughout the race to catch up to the leader.