A racing cyclist, whose mass with his cycle is $75{\text{ }}kg$, works at a rate of $720{\text{ }}W$ while moving on a straight horizontal road. The resistance to the cyclist’s motion is constant and equal to $R{\text{ }}N$.
a) Given that the cyclist is accelerating at $0.16{\text{ }}m{\text{ }}{s^{ - 2}}$ at an instant when his speed is $12{\text{ }}m{\text{ }}{s^{ - 1}}$, find the value of $R$.
b) Given that the cyclist’s acceleration is positive, show that his speed is less than $15{\text{ }}m{\text{ }}{s^{ - 1}}$.
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