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From 100+ hypermiling / ecodriving tips to increase gas mileage - EcoModder.com

49) Conserve momentum: brake hard

It sounds like a contradiction, but there are rare times when braking hard can save fuel compared to coasting or light braking: it's a "damage control" technique when faced with an unpredictable/unanticipated stop or slow down ahead and not a lot of space.

An example: approaching a fresh red traffic light that had no other indicators to predict the change (no pedestrian signal and no cars waiting on the cross street). If you brake lightly/moderately, you will cover the entire distance to the intersection and have no option but coming to a full stop.

But if you brake quite hard initially, you can potentially scrub enough speed and buy enough time to coast the remaining distance to the intersection at a low speed. With judgment and some luck, you'll arrive at a fresh green light and avoid a full stop.

Obviously, rapid deceleration isn't a safe option if there is following traffic.