What should be the spring constant k of a spring designed to bring a 1300 kg car to rest from a speed of 95 km/h so that the occupants undergo a maximum acceleration of 5.0g?

We have that for the Question ,it can be said that he spring constant k of a spring designed to bring a 1300 kg car to rest from a speed of 95 km/h so that the occupants undergo a maximum acceleration of 5.0g is

k=4449.3Nm^{-1}

From the question we are told

What should be the spring constant k of a spring designed to bring a 1300 kg car to rest from a speed of 95 km/h so that the occupants undergo a maximum acceleration of 5.0g?

Generally the equation for the  angular frequency is mathematically given as

Generally the equation for the  spring constant k is mathematically given as

k=4449.3Nm^{-1}

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Spring constant, k = 4485.24 N/m

Explanation:

It is given that,

Mass of the car, m = 1300 kg

Speed of the car, v = 95 km/h = 26.38 m/s

Acceleration, a = 5 g

We need to find the spring constant k of the spring such that,

m a = k x

.........(1)

The elastic potential energy is balanced by the kinetic energy of the spring such that,

k = 4485.24 N/m

So, the spring constant of the spring is 4485.24 N/m. Hence, this is the required solution.