In case of emergency braking, the braking distance of the vehicle should not exceed 30m. How fast can a car move if the coefficient of sliding friction between its tires and the road is 0.5?
Initial data: S (maximum braking distance of the vehicle) = 30 m; μ (coefficient of sliding friction between vehicle tires and road) = 0.5.
Reference values: g (acceleration due to gravity) = 10 m / s ^ 2.
1) Determine the acceleration of the car during braking: m * a = -Ftr. = -μ * m * g.
a = -μ * g = -0.5 * 10 = -5 m / s ^ 2 (slow motion).
2) Determine the speed of the car before braking: S = (V ^ 2 – V0 ^ 2) / 2a = -V0 ^ 2 / 2a.
-V0 ^ 2 = 2a * S; V0 = √- (2a * S) = √- (2 * (-5) * 30) = √300 = 17.32 m / s.
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