A particle has x = at³ − bt, a,b0. From t=0 to t=√(b/a), its average speed is:

Question

A particle has x = at³ − bt, a,b>0. From t=0 to t=√(b/a), its average speed is:

G1 Physics · Accepted Answer

v = 3at²−b. Turning point: t = √[b/(3a)]. At this point, x = −2b√(b/a)/(3√3). At t=0 and t=√(b/a), x=0. Hence total distance = 2 × 2b√(b/a)/(3√3) = 4b√(b/a)/(3√3). Total time = √(b/a). Therefore average speed = 4b/(3√3).