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yuki

  • 5 years ago

A particle is moving on a straight line with velocity v=sqrt(s) where s is the distance from the particle to the origin. When t=0, s =1. What is the value of s when t=1 ?

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  1. Regan
    • 5 years ago
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    v=ds/dt ds/dt=s^1/2 s^-1/2 ds = dt integrate both sides 2*s^1/2=t+c solve for s s^1/2=(t+c)/2 s=((t+c)/2)^2 s=(t^2+2tc+c^2)/4 substitute s(t=0)=1 to find c 1=0+0+(c^2)/4 c=2 full solution: s=(t^2+4t+4)/4 substitute t=1 s=(1+4+4)/4=9/4 : )

  2. Yuki
    • 5 years ago
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    That makes so much sense. So this is a problem that has to do with differential equations, huh? I thought it had something to do with parametric equations, so I couldn't find out how to solve it... Thanks !

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