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 81.7 km/h?
answer in m

To determine the necessary thickness of barriers to safely stop a car, we need to consider the deceleration experienced by the car when it hits the barriers.

First, let's convert the car's speed from kilometers per hour to meters per second:
81.7 km/h = (81.7 * 1000) m / (60 * 60) s = 22.7 m/s

Now, we need to calculate the deceleration required to stop the car. We can use the following equation:

v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s, as the car needs to come to a stop)
u = initial velocity (22.7 m/s)
a = acceleration/deceleration (which we want to find)
s = displacement (unknown)

Rearranging the equation, we get:

a = (v^2 - u^2) / (2s)

Since the car comes to a stop, we have v^2 = 0, and rearranging the equation further, we get:

s = u^2 / (2a)

Substituting the given values, we find:

s = (22.7^2) / (2a)

Now, let's substitute the acceleration with 300 m/s^2, as that is the acceleration a person wearing a safety belt can withstand:

s = (22.7^2) / (2 * 300)

Calculating this expression, we find:

s ≈ 0.381 m

Therefore, the thickness of the barriers needed to safely stop a car traveling at 81.7 km/h is approximately 0.381 meters.