Neco Model Questions Vol1 2017 Mathematics Question 37

A cyclist's speed (in km/h) during the first 8 minutes of a ride is given by the following piecewise linear function: - From t = 0 min to t = 2 min, speed increases uniformly from 0 to 12 km/h. - From t = 2 min to t = 5 min, speed remains constant at 12 km/h. - From t = 5 min to t = 8 min, speed increases uniformly from 12 to 18 km/h. (a) Calculate the total distance travelled during these 8 minutes, in kilometres, correct to two decimal places. (b) The cyclist's energy expenditure (in kilojoules) during the ride is proportional to the integral of the square of the speed with respect to time. If the total energy expended over the 8 minutes is 960 kJ, determine the constant of proportionality \(k\) (in kJ·h·km\(^{-2}\)). Give your answer as a fraction in lowest terms.