A 1.31-kg block slides across a rough surface such that it slows down with an acceleration of 1.39 m/s2. What is the coefficient of kinetic friction between the block and the surface?

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To find the coefficient of kinetic friction between the block and the surface, we can use the equation:

ma = μk * m * g

where
m = mass of the block (1.31 kg)
a = acceleration of the block (-1.39 m/s^2, negative because the block is slowing down)
g = acceleration due to gravity (9.8 m/s^2)
μk = coefficient of kinetic friction (unknown)

Rearranging the equation, we get:

μk = (m * a) / (m * g)

Simplifying further, we have:

μk = a / g

Now, let's substitute the given values into the equation:

μk = (-1.39 m/s^2) / (9.8 m/s^2)

Calculating this gives us:

μk ≈ -0.142

Since the coefficient of friction cannot be negative, we take the absolute value to obtain the final answer:

The coefficient of kinetic friction between the block and the surface is approximately 0.142.