El tiempo de reacción de un conductor de automóvil es 0,75s. Si el automóvil puede experimentar una desaceleracion de 4m/s^2. Calcular la distancia recorrida hasta detenerse una vez recibida la señal, cuando su velocidad era 10m/s

x_total = 20m

Explanation:

This is an exercise in kinematics, we will look for the distance it travels during the reaction time, where there is no braking, and then the distance during the deceleration.

Distance traveled during response time

v = x₁ / t

x₁ = v t

let's calculate

x₁ = 10 0.75

x₁ = 7.5 m

Now we calculate the distance during braking, the final speed is zero (v = 0)

v² = v₀² - 2 a x₂

x₂ = v₀² / 2 a

let's calculate

x₂ = 10² / (2 4)

x₂ = 12.5m

the total stopping distance is

x_total = x₁ + x₂

X_total = 7.5 + 12.5

x_total = 20m