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2Pravocrtno gibanje sa promjenjivim ubrzanjima
Ubrzanje: Odreð ivanje jednad� be pravca
v0 = 0; s0 = 0; t0 = 0; t1 = 1; t2 = 3; t3 = 4;
a1@t_D = InterpolatingPolynomial @880, 0<, 81, 1<<, tDa2@t_D = InterpolatingPolynomial @881, 1<, 83, -1<<, tDa3@t_D = InterpolatingPolynomial @883, -1<, 84, 0<<, tDt
2 - t
-4 + t
sla1 = Plot@a1@tD, 8t, t0, t1<, Filling ® Axis, PlotStyle ® ThickD;sla2 = Plot@a2@tD, 8t, t1, t2<, Filling ® Axis, PlotStyle ® ThickD;sla3 = Plot@a3@tD, 8t, t2, t3<, Filling ® Axis, PlotStyle ® ThickD;Graf1 = Show@8sla1, sla2, sla3<, PlotRange ® 880, t3<, 8-1, 1<<, AxesLabel ® 8t, a@tD<D
1 2 3 4t
-1.0
-0.5
0.5
1.0
aHtL
Brzina
v1@t_D = Integrate@a1@tD, tDv2@t_D = v1@t1D + Integrate@a2@tD, tD - Integrate@a2@tD, 8t, t0, t1<Dv3@t_D = v2@t2D + Integrate@a3@tD, tD - Integrate@a3@tD, 8t, t0, t2<D
t2
2
-1 + 2 t -
t2
2
8 - 4 t +
t2
2
slv1 = Plot@v1@tD, 8t, t0, t1<, Filling ® Axis, PlotStyle ® ThickD;slv2 = Plot@v2@tD, 8t, t1, t2<, Filling ® Axis, PlotStyle ® ThickD;slv3 = Plot@v3@tD, 8t, t2, t3<, Filling ® Axis, PlotStyle ® ThickD;Graf2 = Show@8slv1, slv2, slv3<,
PlotRange ® 880, t3<, 80, 1<<, AxesLabel ® 8t, v@tD<, AspectRatio ® 1 � 2.5D
1 2 3 4t
0.2
0.4
0.6
0.8
1.0
vHtL
Put
s1@t_D = Integrate@v1@tD, tDs2@t_D = s1@t1D + Integrate@v2@tD, tD - Integrate@v2@tD, 8t, t0, t1<Ds3@t_D = s2@t2D + Integrate@v3@tD, tD - Integrate@v3@tD, 8t, t0, t2<D
t3
6
1
3- t + t2 -
t3
6
-
26
3+ 8 t - 2 t2 +
t3
6
s3@t3D
2
2 pravocrtno_gibanje_promjenjivo_ubrzanje.nb
sls1 = Plot@s1@tD, 8t, t0, t1<, Filling ® Axis, PlotStyle ® ThickD;sls2 = Plot@s2@tD, 8t, t1, t2<, Filling ® Axis, PlotStyle ® ThickD;sls3 = Plot@s3@tD, 8t, t2, t3<, Filling ® Axis, PlotStyle ® ThickD;Graf3 = Show@8sls1, sls2, sls3<,
PlotRange ® 880, t3<, 80, 2<<, AxesLabel ® 8t, s@tD<, AspectRatio ® 1 � 2.5D
1 2 3 4t
0.5
1.0
1.5
2.0
sHtL
Rezultati
Graf1
Graf2
Graf3
1 2 3 4t
-1.0
-0.5
0.5
1.0
aHtL
1 2 3 4t
0.2
0.4
0.6
0.8
1.0
vHtL
1 2 3 4t
0.5
1.0
1.5
2.0
sHtL
pravocrtno_gibanje_promjenjivo_ubrzanje.nb 3
