Question

Highway safety engineers build soft barriers so that cars hitting them will slow down at a safe rate. a person wearing a safety belt can withstand an acceleration of 300 m/s 2 . how thick should barriers be to safely stop a car that hits the barriers at 92.8 km/h? answer in units of m.

Answer 1

Basically, we want to see the distance in terms of thickness. So, for this rectilinear motion at constant acceleration, the equation to be used is:

x = v₀t + 0.5at²

First, let's determine t using the equation:
a = |v - v₀|/t
300 m/s² = |0 - 92.8 km/h * 1,000 m/1 km * 1 h/3600 s|/t
t = 0.086 seconds

x = (92.8 km/h * 1,000 m/1 km * 1 h/3600 s)(0.086 s) + 0.5(300 m/s²)(0.086 s)²
x = 3.33 meters