How to Calculate the Stopping Distance of a Car
A car's tires are designed to provide friction between the car and the road. This friction allows the car to accelerate from a stop and to decelerate from high speed. The tires provide grip, allowing the car to safely navigate roadways. When a driver wants to stop the car, he makes a mental estimation of the required stopping distance and applies the brakes at a rate that allows him to stop safely. In emergencies, the driver can apply the brakes firmly to stop in a shorter distance. Today, anti-lock brakes prevent wheels from locking, which could make the car skid.
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Instructions
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Calculate the Stopping Distance of a Car with Locked Wheels
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Determine the coefficient of friction between the tires and the road. If the wheels of the car are locked, the tires are sliding across the pavement and a kinetic coefficient of friction should be used. For tires in good condition and dry pavement, the coefficient of kinetic friction is approximately 0.7. Worn tires, wet roads, or ice can reduce the coefficient of kinetic friction.
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Select an initial velocity for the car with units of feet-per-second. Speeds in MPH can be converted to feet-per-second by multiplying the speed by 1.6.
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Calculate the stopping distance of a car using the following formula: D = V2/μg, where V is the starting speed of the car in feet/sec, μ is the coefficient of kinetic friction between the tires and the road, and g is the acceleration due to gravity. For example, a car traveling at 88 ft/sec (60 mph) on a dry road with good tires will require (88 ft/sec)2/(2 * 0.7 * 32 ft/sec/sec) = 172 feet.
Calculate the Stopping Distance of a Car with Rolling Wheels
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4
Determine the coefficient of friction between the tires and the road. If the wheels of the car are turning, the tires are rolling on the pavement, and not sliding as in the locked wheels example. In this case, a static coefficient of friction should be used. For tires in good condition and dry pavement, the coefficient of static friction is approximately 1.0. Worn tires, wet roads, or ice can reduce the coefficient of static friction.
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Select an initial velocity for the car with units of feet-per-second. Speeds in MPH can be converted to feet-per-second by multiplying the speed by 1.6.
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6
Calculate the stopping distance of a car using the following formula: D = V2/μg, where V is the starting speed of the car in feet/sec, μ is the coefficient of static friction between the tires and the road, and g is the acceleration due to gravity. For example, a car traveling at 88 ft/sec (60 mph) on a dry road with good tires will require (88 ft/sec)2/(2 * 1.0 * 32 ft/sec/sec) = 121 feet.
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