A bicyclist in the Tour de France crests a mountain pass as he moves at 18 kmh. At the bottom 4.0 km farther his speed is 80 kmh. What was his average acceleration (in ms2) while riding down the mount?

To find the average acceleration, we can use the formula ( a = \frac{\Delta v}{\Delta t} ). First, we need to convert the speeds from km/h to m/s: 18 km/h is approximately 5 m/s, and 80 km/h is approximately 22.22 m/s. The change in velocity ((\Delta v)) is (22.22 , \text{m/s} - 5 , \text{m/s} = 17.22 , \text{m/s}). The time taken to travel 4.0 km (4000 m) at an average speed of ( \frac{5 + 22.22}{2} \approx 11.61 , \text{m/s} ) is ( \Delta t \approx \frac{4000}{11.61} \approx 344.4 , \text{s} ). Thus, the average acceleration is ( a \approx \frac{17.22}{344.4} \approx 0.05 , \text{m/s}^2 ).