The leader in a race has 500m to go and is running at a constant speed of 4m/s, but with 100m to go increases her speed by a constant acceleration of 0.1m/s^2. The second runner is 100m behind the leader when the leader has 500m to go, and running at 3.8m/s when she starts to accelerate at a constant rate. Find the minimum acceleration she needs in order to win the race.

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The leader in a race has 500m to go and is running at a constant speed of 4m/s, but with 100m to go increases her speed by a constant acceleration of 0.1m/s^2.

The second runner is 100m behind the leader when the leader has 500m to go, and running at 3.8m/s when she starts to accelerate at a constant rate.

Find the minimum acceleration she needs in order to win the race.

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