Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 92

Drag race of car and motorcycle. A popular web video shows a jet airplane, a car, and a motorcycle racing from rest along a runway (Fig. 2.35). Initially the motorcycle takes the lead, but then the jet takes the lead, and finally the car blows past the motorcycle. Consider the motorcycle−car race. The motorcycle’s constant acceleration \( a_m = 8.40 \text{ m/s}^2 \) is greater than the car’s constant acceleration \( a_c = 5.60 \text{ m/s}^2 \), but the motorcycle has an upper limit of \( v_m = 58.8 \text{ m/s} \) to its speed while the car has an upper limit of \( v_c = 106 \text{ m/s} \). Let the car and motorcycle race in the positive direction of an x axis, starting with their midpoints at \( x = 0 \) at \( t = 0 \). At what (a) time and (b) position are their midpoints again aligned?