The function f,defined by f(t)=6+cos(t/40)+3sin(7t/40),is used to model the velocity of the plane,in

题目

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?

答案

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)...