The driver of a car travels at 90 km / h, observes some children playing on the road 50 m away, and applies the brakes, managing to stop 4 seconds later, if the total mass of the driver-vehicle system is 2200 kg What was the force developed by the brakes? Was there an accident? Explain with mathematical arguments, please help.

13,750 N

Yes

Explanation:

Given:

v₀ = 90 km/h = 25 m/s

v = 0 m/s

t = 4 s

Find: a and Δx

a = Δv / Δt

a = (0 m/s − 25 m/s) / (4 s)

a = -6.25 m/s²

F = ma

F = (2200 kg) (-6.25 m/s²)

F = -13,750 N

Δx = ½ (v + v₀) t

Δx = ½ (0 m/s + 25 m/s) (4 s)

Δx = 50 m

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