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The equation for the stopping distance of a car is the total of the distance travelled while the driver is reacting ‘dR’ so there's no deceleration during this reaction distance plus the distance while the driver is braking, ‘dB’. The reaction distance is going to be the initial speed times the reaction time plus ‘dB’. Let’s figure out an equation for the braking distance, ‘Vf2’ equals ‘V02’ squared plus two ‘a’ times ‘dB‘ and solving for ‘dB’: ‘Vf2’ is zero because the driver is going to stop, then we’ll subtract ‘V02’ and we’ll also divide both sides by two ‘a’ giving us ‘dB’ is: negative ‘V02’ divided by two ‘a’ and substituting we’ll have proven that the total stopping distance is ‘V0’ times the reaction time minus ‘V02’ divided by two ‘a’.
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