As relay runner A enters the 65-ft-long exchange zone with a speed of 30 ft/s, he begins to slow down. He hands the baton to runner B 2.5 s later as they leave the exchange zone with the same veloc - ity. Determine (a) the uniform acceleration of each of the runners, (b) when runner B should begin to run.

a_a = - 3.2 ft/s^2, a_b = 3.723 ft/s^2

t = 5.909 s

Explanation:

Given:

- Initial velocity of A v_i, a = 30 ft / s

- Initial distance s_o = 0

- Length of the exchange zone s_f = 65 ft

- Time taken t = 2.5 s

Start out by A's velocity as he gets to the end of the exchange zone.

Part a

Runner A decelerates at a uniform rate, so you can use the equation:

s_f = s_o + v_i, a*t + 0.5a_a*t^2

65 = 0 + 30*2.5 + 0.5*a_a*2.5^2

a_a = - 20 / 2.5^2

a _a = - 3.2 ft/s^2

Runner B accelerates at v_f, a as final velocity at a uniform rate, so you can use the equation:

v_f, b^2 - v_i, b^2 = 2*a_b*s

a_b = (30 - 3.2*2.5) ^2 / 2*65

a_b = 3.723 ft/s^2

Part b

When Runner B should begin running:

t = (v_f, b - v_i, b) / a_b

t = (30 - 3.2*2.5) / 3.723

t = 5.909 s