Question

求解一道AP 微积分题目，急急急！！！！求详细过程

The function f, defined by f(t)=6+cos(t/40)+3sin(7t/40), is used to model the velocity of the plane, in miles per minute, for 0≤t≤40. According to thhis model, waht is the acceleration of the plane at t=23? What is the average velocity of the plane, in miles per minute, over the time interval 0≤t≤40?

Answer 1

据定义，加速度就是速度对时间的微分，故加速度函数为
a(t)=f'(t)=-1/40*sin(t/40)+21/40*cos(7t/40)，把t=23带入即得23分时的加速度
a=-0.347miles per minute^2
路程是速度对时间的积分，因此平均速度为
v1=1/40*∫(0→40)f(t)dt=(6t+40*sin(t/40)-120/7*cos(7t/40))|(40→0)=6.97miles per minute