Question

an automobile with 0.320 m radius tires travels 85,000 km before wearing them out. how many revolutions do the tires make, neglecting any backing up and any change in radius due to wear? rev

Explanation:

Step1: Convert the distance to meters

The distance \(d = 85000\space km=85000\times10^{3}\space m = 8.5\times 10^{7}\space m\)

Step2: Calculate the circumference of the tire

The circumference of a circle is \(C = 2\pi r\), where \(r = 0.320\space m\). So \(C=2\pi\times0.320\space m\approx 2.01\space m\)

Step3: Find the number of revolutions

The number of revolutions \(N=\frac{d}{C}\). Substitute \(d = 8.5\times 10^{7}\space m\) and \(C\approx2.01\space m\) into the formula: \(N=\frac{8.5\times 10^{7}}{2.01}\approx4.23\times 10^{7}\)

Answer:

\(4.23\times 10^{7}\)