✔ 最佳答案
a. A所走的距離
= S (t = 0 → 10) t(10 - t) dt
= S (t = 0 → 10) (-t2 + 10t) dt
= [-t3/3 + 5t2] (t = 0 → 10)
= 500/3 m
B所走的距離
= S (t = 0 → 10) 1/5 t2(10 - t) dt
= 1/5 S (t = 0 → 10) (-t3 + 10t2) dt
= 1/5 [-t4/4 + 10t3/3](t = 0 → 10)
= 500/3 m
車A,
dv(t)/dt = -t + 10 - t = 10 - 2t
d2v(t)/dt2 = -2 < 0
設dv(t)/dt = 0, t = 5
所以,t = 5,車A是最高速度 = 5(10 - 5) = 25 m/s
車B,
dv(t)/dt = 1/5 [2t(10 - t) - t2] = 1/5 (-3t2 + 20t)
d2v(t)/dt2 = 1/5 (-6t + 20)
dv(t)/dt = 0, t = 0 或 20/3
當t = 0,d2v(t)/dt2 = 4 > 0
當t = 20/3,d2v(t)/dt2 = -4 < 0
所以,當t = 20/3,車B是最高速度 = 1/5 (20/3)2(10 - 20/3) = 800/27 m/s