A particle has x = at³ − bt², a,b0. During 0 ≤ t ≤ b/a, the average speed is:

Question

A particle has x = at³ − bt², a,b>0. During 0 ≤ t ≤ b/a, the average speed is:

G1 Physics · Accepted Answer

v = 3at²−2bt = t(3at−2b). The non-zero turning time is t = 2b/(3a). x(0)=0, x[2b/(3a)] = −4b³/(27a²), x(b/a)=0. Total distance = 8b³/(27a²). Total time = b/a. Average speed = [8b³/(27a²)]/(b/a) = 8b²/(27a).