a(t) = 20*exp(-0.05*t) - 9.8
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almost_v(t) = integral( a(t), t)
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almost_v(t)
-9.8*t - 400.0*e^(-0.05*t) -9.8*t - 400.0*e^(-0.05*t) |
almost_v(0)
-400.0 -400.0 |
v(t)=almost_v(t) + 400
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v(t)
-9.8*t - 400.0*e^(-0.05*t) + 400 -9.8*t - 400.0*e^(-0.05*t) + 400 |
almost_h(t) = integral( v(t), t)
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almost_h(t)
-4.9*t^2 + 400*t + 8000.0*e^(-0.05*t) -4.9*t^2 + 400*t + 8000.0*e^(-0.05*t) |
almost_h(0)
8000.0 8000.0 |
h(t)=almost_h(t)-8000
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h(t)
-4.9*t^2 + 400*t + 8000.0*e^(-0.05*t) - 8000 -4.9*t^2 + 400*t + 8000.0*e^(-0.05*t) - 8000 |
find_root(v(t)==0, 1, 100)
32.963065202764675 32.963065202764675 |
h(_)
1400.30333031 1400.30333031 |
find_root(h(t)==0, 1, 100)
53.007513640052935 53.007513640052935 |
v(_)
-147.723503935 -147.723503935 |
plot(a(t),0,53)
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plot(v(t),0,53)
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plot(h(t),0,53)
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j(t)=derivative(a(t), t)
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j(t)
-e^(-0.0500000000000000*t) -e^(-0.0500000000000000*t) |
plot( j(t), 0, 53)
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