# In case of emergency braking, the braking distance of the vehicle should not exceed 30m.

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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