Ordinary Differential Equation
2014-02-28 3:03 am
The resistance force on a body is directly proportional to the velocity of the body. Set up a differential equation and find the velocity of a body of mass 2.4 kg after 10 s given its initial velocity 30 ms-1 and constant of proportionality 0.7 kgs-1 .
回答 (1)
2014-02-28 5:04 am
✔ 最佳答案
F=2.4a=-0.7v2.4(dv/dt)=-0.7v
2.4∫(dv/v)=-0.7∫dt
2.4ln[v]=-0.7t+C
v=Ce^(-7t/24)
t=0,v=30
30=Ce^(0)
C=30
v=30e^(-7t/24)
Negative sign means that the resistance force is opposite to the velocity.
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