Please show me how to solve this problem. A person wearing a shoulder harness can survive a car crash if the acceleration is less that -300 m/s2. How far must the front end collapse if it crashes while going 101 km/hr?

Thanks.

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101 km/h = 28.06 m/s

To decelerate from velocity V in a distance X at a rate of a = 300 m/s^2,
V = sqrt(2 a X)

X = V^2/(2 a) = 1.3 meters

This assumes the crash is into an immovable object, so that all deceleration is achieved by collapsing the front end. A collision with another car or a soft barrier might have a different result. This is a good approximation for a head-on collision with a similar car.

how do i do this problem

The Math Behind the Law How much force is Mike applying to the 1000 kg car to make it accelerate at a rate of .05 m/s2?

To solve this problem, we need to convert the given speed from kilometers per hour to meters per second, and then use the kinematic equation to find the distance.

Step 1: Convert the speed from km/hr to m/s.
To convert from kilometers per hour (km/hr) to meters per second (m/s), we need to multiply by the conversion factor of 1000/3600. This is because there are 1000 meters in a kilometer and 3600 seconds in an hour.

Given speed: 101 km/hr

101 km/hr * (1000 m/km) / (3600 s/hr) = 28.06 m/s (rounded to two decimal places)

So, the speed is approximately 28.06 m/s.

Step 2: Use the kinematic equation to find the distance.
The kinematic equation we will use is:

v² = u² + 2as

Where:
v = final velocity (0 m/s since the car comes to rest)
u = initial velocity (28.06 m/s)
a = acceleration (-300 m/s²)
s = distance (what we need to find)

Rearrange the equation to solve for s:

s = (v² - u²) / (2a)

Plugging in the values:

s = (0² - (28.06 m/s)²) / (2 * -300 m/s²)

Calculate the expression inside the parentheses first:

s = (-789.24 m²/s²) / (-600 m/s²)

Divide to find the distance:

s = 1.3154 m

So, the front end of the car must collapse approximately 1.3154 meters during the crash for the person wearing the shoulder harness to survive.

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