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You could stop at 20 miles per hour without hitting him.

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Assuming The Highway Code formula for stopping distances:

stopping_distance = thinking distance + stopping time

= speed + speed²/20 ft (where speed is in mph)

→ 65 = speed + speed²/20

→ speed² + 20speed + 1300 = 0

→ speed = -10 + 10√14 mph ≈ 27.4 mph

(The negative square root can be ignored as it gives a negative speed which is nonsense for this problem.)

However, this assumes that you observe, think and can start braking within 15/22 (≈ 0.68) seconds of the child running into the road (1ft for every 1 mph of speed), and your braking matches the Highway Code assumptions for good tyres, brakes and dry road conditions.

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