Ответы
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1)
![v(t)=s'(t)=(0.5t^2-4t)'=t-4 v(t)=s'(t)=(0.5t^2-4t)'=t-4](https://tex.z-dn.net/?f=v%28t%29%3Ds%27%28t%29%3D%280.5t%5E2-4t%29%27%3Dt-4)
2)
![v(t)=s'(t)=(4t^2-5t+7)'=8t-5 v(t)=s'(t)=(4t^2-5t+7)'=8t-5](https://tex.z-dn.net/?f=v%28t%29%3Ds%27%28t%29%3D%284t%5E2-5t%2B7%29%27%3D8t-5)
![v(2)=8*2-5=11 v(2)=8*2-5=11](https://tex.z-dn.net/?f=v%282%29%3D8%2A2-5%3D11)
3)
![a(t)=v'(t)=s''(t)=(-t^3+2t^2)''=(-3t^2+4t)'=-6t+4 a(t)=v'(t)=s''(t)=(-t^3+2t^2)''=(-3t^2+4t)'=-6t+4](https://tex.z-dn.net/?f=a%28t%29%3Dv%27%28t%29%3Ds%27%27%28t%29%3D%28-t%5E3%2B2t%5E2%29%27%27%3D%28-3t%5E2%2B4t%29%27%3D-6t%2B4)
![a(5)=-6*5+4=-26 a(5)=-6*5+4=-26](https://tex.z-dn.net/?f=a%285%29%3D-6%2A5%2B4%3D-26)
4)
![v(t)=6t^2+2t v(t)=6t^2+2t](https://tex.z-dn.net/?f=v%28t%29%3D6t%5E2%2B2t)
![6t^2+2t=104 6t^2+2t=104](https://tex.z-dn.net/?f=6t%5E2%2B2t%3D104)
![6t^2+2t-104=0 6t^2+2t-104=0](https://tex.z-dn.net/?f=6t%5E2%2B2t-104%3D0)
![(2t-8)(3t+13)=0 (2t-8)(3t+13)=0](https://tex.z-dn.net/?f=%282t-8%29%283t%2B13%29%3D0)
![t_1=4 t_1=4](https://tex.z-dn.net/?f=t_1%3D4)
![t_2=- frac{13}{3} t_2=- frac{13}{3}](https://tex.z-dn.net/?f=t_2%3D-+frac%7B13%7D%7B3%7D+)
5)
![F=ma(t)=mx''(t)=10*(-2sin(2 pi t))''=10*8 pi ^2*sin(2 pi t) F=ma(t)=mx''(t)=10*(-2sin(2 pi t))''=10*8 pi ^2*sin(2 pi t)](https://tex.z-dn.net/?f=F%3Dma%28t%29%3Dmx%27%27%28t%29%3D10%2A%28-2sin%282+pi+t%29%29%27%27%3D10%2A8+pi+%5E2%2Asin%282+pi+t%29)
![F(0.25)=10*8 pi ^2*sin(2 pi*0.25)=10*8 pi ^2*sin( frac{ pi }{2} )=80 pi ^2 F(0.25)=10*8 pi ^2*sin(2 pi*0.25)=10*8 pi ^2*sin( frac{ pi }{2} )=80 pi ^2](https://tex.z-dn.net/?f=F%280.25%29%3D10%2A8+pi+%5E2%2Asin%282+pi%2A0.25%29%3D10%2A8+pi+%5E2%2Asin%28+frac%7B+pi+%7D%7B2%7D+%29%3D80+pi+%5E2)
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