搜搜做题作业网一道英语的微积分问题The displacement (in centimeters) of a particle mo
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一道英语的微积分问题
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 4 cos πt,where t is measured in seconds.(Round your answers to two decimal places.)
(a) Find the average velocity during each time period.
(i) [1,2]
cm/s
(ii) [1,1.1]
cm/s
(iii) [1,1.01]
cm/s
(iv) [1,1.001]
cm/s
(b) Estimate the instantaneous velocity of the particle when t = 1.
cm/s
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 4 cos πt,where t is measured in seconds.(Round your answers to two decimal places.)
(a) Find the average velocity during each time period.
(i) [1,2]
cm/s
(ii) [1,1.1]
cm/s
(iii) [1,1.01]
cm/s
(iv) [1,1.001]
cm/s
(b) Estimate the instantaneous velocity of the particle when t = 1.
cm/s
求平均速度是么
s = 2sinπt+4cosπt
V(1-2)=(S2-S1)/(2-1)=(0+4)-(0-4)=8
同理V(1-1.1)=[2sin(1.1π)+4cos(1.1π)+4]/0.1≈4.22
V(1-1.01)=[2sin(1.01π)+4cos(1.01π)+4]/0.01≈6.08
V(1-1.001)=[2sin(1.001π)+4cos(1.001π)+4]/0.001≈6.26
s = 2sinπt+4cosπt
v=ds/dt=2πcosπt-4πsinπt
瞬时速度v1=2π*1-4π*0=2π
再问： 额...就V(1-2)=(S2-S1)/(2-1)=(0+4)-(0-4)=8，这个答案是对的。。 (0+4)-(0-4)是怎么算出来的？
再答： t=2秒的时候 S2= 2sin2π+4cos2π=0+4=4 t=1秒的时候 S1=2sinπ+4cosπ=0-4=-4 所以平均速度等于总位移除以时间 v平均=(S2-S1)/(2-1)=8 我看了一下，应该是我马虎了，下面的结果都少了个负号 对吗？
s = 2sinπt+4cosπt
V(1-2)=(S2-S1)/(2-1)=(0+4)-(0-4)=8
同理V(1-1.1)=[2sin(1.1π)+4cos(1.1π)+4]/0.1≈4.22
V(1-1.01)=[2sin(1.01π)+4cos(1.01π)+4]/0.01≈6.08
V(1-1.001)=[2sin(1.001π)+4cos(1.001π)+4]/0.001≈6.26
s = 2sinπt+4cosπt
v=ds/dt=2πcosπt-4πsinπt
瞬时速度v1=2π*1-4π*0=2π
再问： 额...就V(1-2)=(S2-S1)/(2-1)=(0+4)-(0-4)=8，这个答案是对的。。 (0+4)-(0-4)是怎么算出来的？
再答： t=2秒的时候 S2= 2sin2π+4cos2π=0+4=4 t=1秒的时候 S1=2sinπ+4cosπ=0-4=-4 所以平均速度等于总位移除以时间 v平均=(S2-S1)/(2-1)=8 我看了一下，应该是我马虎了，下面的结果都少了个负号 对吗？
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