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## Homework Statement

A 100 kg object is accelerated by a force of 10,000 N. What is the acceleration of the object caused by the force?

## Homework Equations

F_N = m * u(a / a_0) * a

a_0 = 1.2 * 10^-8 cm / s^2

## The Attempt at a Solution

I'm using u(a / a_0) = 1 / (1 + a_0 / a) as my interpolating function.

This gives F_N = m * a / (1 + a_0 / a)

10,000 N = (100 kg) * a / (1 + (1.2 * 10^-8 cm/s^2) / a)

10,000 N / 100 kg = a^2 / (a + (1.2 * 10^-8 cm/s^2))

a^2 - (10,000 N / 100 kg) * a - (10,000 N / 100 kg) * (1.2 * 10^-8 cm/s^2) = 0

Applying quadratic formula:

a = ((10,000 N / 100 kg) +/- sqrt((10,000 N / 100 kg)^2 + 4*(10,000 N / 100 kg)*((10,000 N / 100 kg) * (1.2 * 10^-8 cm/s^2)))) / 2

Which comes out (cleanly I might add) to a number slightly smaller than 100 m/s^2: 99.999999988 m/s^2

This was the query I gave Google for calculating this: "(100 + sqrt(10000 - 4 * (1.2 * 10^-6))) / 2"

The answer in the book is 100 m /s^2.

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