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?
need final snswer in m

To find out how thick the barriers should be to safely stop a car, we need to use the concept of deceleration. Deceleration is the rate at which an object slows down or comes to a stop.

Given information:
- The acceleration that a person wearing a safety belt can withstand is 300 m/s^2.
- The speed of the car that hits the barriers is 81.7 km/h.

First, let's convert the speed from km/h to m/s.

1 km/h = 0.2778 m/s

81.7 km/h * 0.2778 m/s = 22.69426 m/s (approx.)

Now, we can calculate the deceleration of the car using the formula:

Deceleration (a) = (Final velocity - Initial velocity) / Time

Since the car comes to a stop, the final velocity is 0 m/s. The initial velocity is 22.69426 m/s.

a = (0 - 22.69426) / Time

To determine the time taken to decelerate, we need to factor in the distance traveled while decelerating. We'll assume the distance is equal to the barrier thickness (d).

The formula to calculate time is:

Time (t) = Distance (d) / Initial velocity

Substituting the values, we get:

t = d / 22.69426

Substituting this value of time back into the deceleration formula:

a = (0 - 22.69426) / (d / 22.69426)

Simplifying further, we get:

a = -22.69426^2 / d

Now, we can solve for d, which represents the barrier thickness:

d = -22.69426^2 / a

Substituting the given acceleration capacity of a person wearing a safety belt (300 m/s^2) into the equation:

d = -22.69426^2 / 300

Calculating this, we find:

d ≈ -514.9054 / 300

d ≈ -1.71635 m

Since we are dealing with distances, the thickness of the barrier cannot be negative. Therefore, we take the absolute value:

d ≈ 1.71635 m

So, the thickness of the barriers should be approximately 1.71635 meters to safely stop a car hitting the barriers at 81.7 km/h.