A block accelerates down an incline angled at $35^{\circ}$ with acceleration magnitude $a=g / 4$, as shown. What is the coefficient of kinetic friction between the block and incline? Assume the acceleration due to gravity is $a_{y}=-g$.
0.45
1.2
0.71
0.37

Step 1 ：The acceleration of the block down the incline is given by the equation: \(a = g \sin(\theta) - \mu_k g \cos(\theta)\)

Step 2 ：We are given that \(a = g / 4\) and \(\theta = 35^\circ\), and we are asked to find \(\mu_k\)

Step 3 ：We can rearrange the equation to solve for \(\mu_k\): \(\mu_k = (g \sin(\theta) - a) / (g \cos(\theta))\)

Step 4 ：Substitute the given values into this equation to find the value of \(\mu_k\)

Step 5 ：Given that \(g = 9.81\), \(a = 2.4525\), and \(\theta = 0.6108652381980153\), we find that \(\mu_k = 0.39501389101934575\)

Step 6 ：\(\boxed{\text{Final Answer: The coefficient of kinetic friction between the block and incline is approximately 0.40. The closest answer choice to this value is 0.37}}\)