# physics

a typical automobile has a maximum deceleration of about 7m/s2, the typical reaction time to engage the brakes is 0.50s. A school board sets the speed limit in a school zone to meet the condition that all cars should be able to stop in a distance of 4 m. a) what maximum speed should be allowed for a typical automobile? b) What fraction of the 4 m is due to the reaction time?

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1. a)
Reaction time distance + Deceleration distance = 4 m
Vmax*(0.5s) + [(Vmax)/2]*Vmax/a = 4 m
0.5 Vmax + Vmax^2/14 = 4

Vmax = 4.78 m/s = 17.2 km/h = 10.7 mph

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