Serway & Jewett — Motion in One Dimension: Problem 37

At \( t = 0 \), one athlete in a race running on a long, straight track with a constant speed \( v_1 \) is a distance \( d_1 \) behind a second athlete running with a constant speed \( v_2 \). (a) Under what circumstances is the first athlete able to overtake the second athlete? (b) Find the time \( t \) at which the first athlete overtakes the second athlete, in terms of \( d_1 \), \( v_1 \), and \( v_2 \). (c) At what minimum distance \( d_2 \) from the leading athlete must the finish line be located so that the trailing athlete can at least tie for first place? Express \( d_2 \) in terms of \( d_1 \), \( v_1 \), and \( v_2 \) by using the result of part (b).