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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.

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jolis1796

Answer:

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

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