You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50 km/h. A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. Calculate the average force exerted on the car by the barrier. Calculate the average deceleration of the car.

F = - 138889 N

a = - 92.59 m/s²

Explanation:

If

vi = 50 Km/h = (50 Km/h) (1000 m / 1 Km) (1 h / 3600 s) = 13.88 m/s

m = 1500 Kg

Δt = 0.15 s

vf = 0 Km/h

F = ?

a = ?

We can apply the Impulse-Momentum Theorem as follows:

F*Δt = m*Δv ⇒ F*Δt = m * (vf - vi) ⇒ F = m * (vf - vi) / Δt

⇒ F = (1500 Kg) * (0 m/s - 13.88 m/s) / (0.15 s)

⇒ F = - 138889 N

Then, we use Newton's 2nd Law:

F = m*a ⇒ a = F / m = ( - 138889 N) / (1500 Kg)

⇒ a = - 92.59 m/s²