For x = t⁴ − 8t² during 0 ≤ t ≤ 4 s, the ratio of average speed to magnitude of average velocity is:

Question

G1 Physics · Accepted Answer

v = 4t(t²−4), so the non-zero turning point is t=2 s. x(0)=0, x(2)=16−32=−16, x(4)=256−128=128. Total distance = 16 + 144 = 160 m. Magnitude of displacement = 128 m. Therefore ratio = 160/128 = 5/4.