A particle moves according to x = at² − bt, where a,b0. During the interval 0 ≤ t ≤ b/a, its average speed is:

Question

A particle moves according to x = at² − bt, where a,b>0. During the interval 0 ≤ t ≤ b/a, its average speed is:

G1 Physics · Accepted Answer

Velocity: v = dx/dt = 2at−b. The turning point occurs at t = b/(2a). Positions: x(0)=0, x[b/(2a)] = −b²/(4a), x(b/a)=0. Total distance = b²/(4a) + b²/(4a) = b²/(2a). Total time = b/a. Average speed = [b²/(2a)]/(b/a) = b/2.