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¸Ðл²ÎÓ룬ӦÖúÖ¸Êý +1
r(t) = 2.0t i +£¨19.0 - 2.0 t^2£©j£¬v(t) = dr/dt = 2.0 i - 4.0 t j, a(t) = dv/dt = -4.0 j, |v(t)| = sqrt(4 + 16t^2)
(1£©
ÔÚt1=1.0sµ½t2=2.0sʱ¼äÄ򵀮½¾ùËÙ¶È = [r(2) - r(1)]/(2-1) = (2.0 i + 6.0 j) m/s

£¨2£©t1=1.0sʱµÄËÙ¶È = v(1) = (2.0 i - 4.0 j ) m/s
ÇÐÏò¼ÓËÙ¶È a_t = d|v|/dt = 16t/sqrt(4 + 16t^2), ÔÚ t =1.0 s, a_t = 16/sqrt(20) = 8/sqrt(5) m/s^2
·¨Ïò¼ÓËÙ¶È a_n = sqrt(a^2 - a_t^2) = sqrt(16 - 64/5) = 4/sqrt(5) m/s^2

£¨3£©t=1.0sʱÖʵãËùÔÚ´¦¹ìµÀµÄÇúÂʰ뾶¦Ñ:
a_n = v^2/¦Ñ, |v(1)|^2 = 4 + 16 = 20, so ¦Ñ = |v|^2/a_n = 20sqrt(5)/4 = 5sqrt(5) m
2Â¥2014-01-27 13:42:54
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¸Ðл²ÎÓ룬ӦÖúÖ¸Êý +1
(1£©Ë²Ê±ËÙ¶ÈV=dr/dt=2.0*i-4*t*j
      Æ½¾ùËÙ¶ÈVp=1/(t2-t1)*Integal{V*dt,t1,t2}
                      =1/(2-1)*Integal{(2*i-4*t*j)*dt,1,2}
                      =2*i-6*j  m/s
(2)t1=1ʱ£¬V=2*i-4*j  m/s
    ´Ëʱ¼ÓËÙ¶Èa=dV/dt=0*i-4*j   m/s^2
    Î»ÒÆÇúÏߵĵ¼Êýy'=dy/dx=(dy/dt)/(dx/dt)=-4*t/2=-2*t
     Î»ÒÆÇúÏßµÄÇÐÏòÁ¿T=£û1£¬-2*t£ý
    µ¥Î»»¯ºóT={1/sqrt(1+4*t^2),-2*t/sqrt(1+4*t^2)}
   Î»ÒÆÇúÏߵķ¨ÏòÁ¿N=£û2*t/sqrt(1+4*t^2)£¬1/sqrt(1+4*t^2)£ý
    ÇÐÏò¼ÓËÙ¶ÈaT=a¡¤T=0 +8/sqrt(5)=8/sqrt(5)  m/s^2
       ·¨Ïò¼ÓËÙ¶ÈaN=a¡¤N=0-4/sqrt(5)=-4/sqrt(5)  m/s^2  
(3)  ÇúÂʰ뾶¦Ñ=Power{1+y'^2 , 3/2}/abs(y'')
                    =5^(3/2)/abs{[dy'/dt]/[dx/dt]}
                     =5^(3/2)/abs[-2/2]=5^(3/2)   m
3Â¥2014-01-27 15:59:45
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