The Physics Behind an Automobile Accident Analysis
Analyze the Speed of Car A Before Braking
The speed of car A at the moment he began braking is 91.8 Km/h. Explanation: We must start this exercise at the end. Let's look for the lighter car acceleration (B). For this, we use Newton's second law: fr = m * a a = fr / m fr = μ * N N-W = 0 Let's replace: a = μ * m * g / m a = μ * g a = 0.8 * 9.8 a = 7.84 m/s² Since car B reached an initial velocity vo₀₂ and at the end the speed was zero, let's use kinematics: v₀₂ = 2 * a * x₂ v₀₂ = √(2 * 7.84 * 26) v₀₂ = 20.19 m/s Let's perform the same procedure for car A. The acceleration is the same as it does not depend on the mass of the vehicles: v₀₁ = √(2 * a * x₁) v₀₁ = √(2 * 7.84 * 19) v₀₁ = 17.36 m/s Now, let's use momentum conservation where the system is the two vehicles: Initial momentum before the crash: p₀ = M * v₁ + 0 After the crash: p_{f} = M * v₀₁ + m * v₀₂ p₀ = p_{f} M * v₁ = M * v₀₁ + m * v₀₂ v₁ = v₀₁ + m / M * v₀₂ v₁ = 17.36 + 1841/3000 * 20.19 v₁ = 20.75 m/s Lastly, to find the speed of car A when the brakes were applied (v): v₁² = v² - 2 * a * x₁ v = √(v₁² + 2 * a * x₁) v = √(20.75² + 2 * 7.84 * 14) v = 25.50 m/s v = 25.50 m/s (1 km/1000 m) * (3600 s/1 h) v = 91.8 Km/h