nerovnoměrný přímočarý pohyb

Nerovnomrn pmoar pohyb

Nerovnomrn pmoar pohybPi rovnomrnm pmoarm pohybu se ujet drha mn pmo mrn s asemt = 0 mint = 10 mint = 20 mint = 30 min

Nerovnomrn pmoar pohybt = 0 st = 1 st = 2 st = 3 st = 4 sPi stejnomrn zrychlenm pmoarm pohybu se rychlost mn pmo mrn s asem

Nerovnomrn pmoar pohybt = 150 st = 151 st = 152 st = 153 st = 154 sZaal brzditPustil brzdua = ?a = ?0 ms-2

Zrychlen pmoarho pohybuTleso zrychlujeZrychlen m stejn smr jako rychlost Tleso zpomalujeZrychlen m opan smr ne rychlost Pozn. : zporn velikost zrychlen pi vpotu naznauje, e zrychlen m opan smr ne rychlost a tleso tedy zpomaluje.

Prmrn rychlost

Prmrn rychlost51015202530354036912451550t [min]s [km]Cyklista vyrazil z jedn vesnice do druh svou obvyklou cestovn rychlost, dky kter si mezi svmi vrstevnky vyslouil pezdvku chrt. Po pti minutch jzdy dorazil ke kopci a zpomalil. Na vrcholu kopce zastavil, pt minut studoval mapu a znovu vyrazil (po rovin). Po dalch deseti minutch jzdy, kdy u ml bt zaruen ve svm cli, znovu zastavil a dalch pt minut studoval mapu. Zjistil, e na kopci patn odboil a musel se tedy vrtit. Pot, co se vydal sprvnou cestou, dojel do svho cle za pt minut. Jak byla jeho prmrn rychlost celkem a na danch secch?

Drha pi rovnomrn zrychlenm pmoarm pohybu

Pokus drha volnho pduTleso padajc volnm pdem (rovnomrn zrychlenm pohyb)Ultrazvukov dlkomrPota zaznamen vzdlenost tlesa od senzoru 20x za vteinu.

Drha pi rovnomrn zrychlenm pmoarm pohybu t [s]s [m]Je evidentn, e vzdlenost pi rovnomrn zrychlenm pohybu neroste pmo mrn s asem. Jak je tedy matematick vyjden zvislosti drhy na ase v tomto ppad?

Graf1

0

0.0122625

0.04905

0.1103625

0.1962

0.3065625

0.44145

0.6008625

0.7848

0.9932625

1.22625

1.4837625

1.7658

2.0723625

2.40345

2.7590625

3.1392

3.5438625

3.97305

4.4267625

4.905

5.4077625

5.93505

6.4868625

7.0632

7.6640625

8.28945

8.9393625

9.6138

10.3127625

11.03625

as [s]

Vzdlenost [m]

Zvislost drhy na ase pi volnm pdu

List1

9.81ts=0,5*a*t*t

00.000

0.050.012

0.10.049

0.150.110

0.20.196

0.250.307

0.30.441

0.350.601

0.40.785

0.450.993

0.51.226

0.551.484

0.61.766

0.652.072

0.72.403

0.752.759

0.83.139

0.853.544

0.93.973

0.954.427

14.905

1.055.408

1.15.935

1.156.487

1.27.063

1.257.664

1.38.289

1.358.939

1.49.614

1.4510.313

1.511.036

1.5511.784

1.612.557

1.6513.354

1.714.175

1.7515.022

1.815.892

1.8516.787

1.917.707

1.9518.651

219.620

2.0520.613

2.121.631

2.1522.673

2.223.740

2.2524.832

2.325.947

2.3527.088

2.428.253

2.4529.442

2.530.656

2.5531.895

2.633.158

2.6534.445

2.735.757

2.7537.094

2.838.455

2.8539.841

2.941.251

2.9542.686

344.145

3.0545.629

3.147.137

3.1548.670

3.250.227

3.2551.809

3.353.415

3.3555.046

3.456.702

3.4558.382

3.560.086

3.5561.815

3.663.569

3.6565.347

3.767.149

3.7568.977

3.870.828

3.8572.704

3.974.605

3.9576.530

478.480

4.0580.454

4.182.453

4.1584.476

4.286.524

4.2588.597

4.390.693

4.3592.815

4.494.961

4.4597.131

4.599.326

4.55101.546

4.6103.790

4.65106.058

4.7108.351

4.75110.669

4.8113.011

4.85115.378

4.9117.769

4.95120.185

5122.625

5.05125.090

5.1127.579

5.15130.093

5.2132.631

5.25135.194

5.3137.781

5.35140.393

5.4143.030

5.45145.691

5.5148.376

5.55151.086

5.6153.821

5.65156.580

5.7159.363

5.75162.172

5.8165.004

5.85167.861

5.9170.743

5.95173.649

6176.580

6.05179.535

6.1182.515

6.15185.519

6.2188.548

6.25191.602

6.3194.679

6.35197.782

6.4200.909

6.45204.060

6.5207.236

6.55210.437

6.6213.662

6.65216.911

6.7220.185

6.75223.484

6.8226.807

6.85230.155

6.9233.527

6.95236.924

7240.345

7.05243.791

7.1247.261

7.15250.756

7.2254.275

7.25257.819

7.3261.387

7.35264.980

7.4268.598

7.45272.240

List1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

as [s]

Vzdlenost [m]


List2

List3

Odvozen zvislosti drhy na ase pi r.z.p.p.0,20,40,60,81,01,21,41,651015201,8252,0t [s]v [m/s]a = 10 ms-2 Okamit rychlostv = a . t Rychlost se mn. Jakou prmrnou rychlost se tleso pohybovalo a do uritho asu?v1 = 0 v2 = v Nov typ grafuZvislost rychlosti na ase pi rovnomrn zrychlenm pohybu

Odvozen zvislosti drhy na ase pi r.z.p.p.0,20,40,60,81,01,21,41,651015201,8252,0t [s]a = 10 ms-2 Rychlost se mn. Jakou drhu urazilo tleso touto prmrnou rychlost?Okamit rychlostv = a . t

Odvozen zvislosti drhy na ase pi r.z.p.p.

Graf1

0

0.0122625

0.04905

0.1103625

0.1962

0.3065625

0.44145

0.6008625

0.7848

0.9932625

1.22625

1.4837625

1.7658

2.0723625

2.40345

2.7590625

3.1392

3.5438625

3.97305

4.4267625

4.905

5.4077625

5.93505

6.4868625

7.0632

7.6640625

8.28945

8.9393625

9.6138

10.3127625

11.03625

as [s]

Vzdlenost [m]


List1

9.81ts=0,5*a*t*t

00.000

0.050.012

0.10.049

0.150.110

0.20.196

0.250.307

0.30.441

0.350.601

0.40.785

0.450.993

0.51.226

0.551.484

0.61.766

0.652.072

0.72.403

0.752.759

0.83.139

0.853.544

0.93.973

0.954.427

14.905

1.055.408

1.15.935

1.156.487

1.27.063

1.257.664

1.38.289

1.358.939

1.49.614

1.4510.313

1.511.036

1.5511.784

1.612.557

1.6513.354

1.714.175

1.7515.022

1.815.892

1.8516.787

1.917.707

1.9518.651

219.620

2.0520.613

2.121.631

2.1522.673

2.223.740

2.2524.832

2.325.947

2.3527.088

2.428.253

2.4529.442

2.530.656

2.5531.895

2.633.158

2.6534.445

2.735.757

2.7537.094

2.838.455

2.8539.841

2.941.251

2.9542.686

344.145

3.0545.629

3.147.137

3.1548.670

3.250.227

3.2551.809

3.353.415

3.3555.046

3.456.702

3.4558.382

3.560.086

3.5561.815

3.663.569

3.6565.347

3.767.149

3.7568.977

3.870.828

3.8572.704

3.974.605

3.9576.530

478.480

4.0580.454

4.182.453

4.1584.476

4.286.524

4.2588.597

4.390.693

4.3592.815

4.494.961

4.4597.131

4.599.326

4.55101.546

4.6103.790

4.65106.058

4.7108.351

4.75110.669

4.8113.011

4.85115.378

4.9117.769

4.95120.185

5122.625

5.05125.090

5.1127.579

5.15130.093

5.2132.631

5.25135.194

5.3137.781

5.35140.393

5.4143.030

5.45145.691

5.5148.376

5.55151.086

5.6153.821

5.65156.580

5.7159.363

5.75162.172

5.8165.004

5.85167.861

5.9170.743

5.95173.649

6176.580

6.05179.535

6.1182.515

6.15185.519

6.2188.548

6.25191.602

6.3194.679

6.35197.782

6.4200.909

6.45204.060

6.5207.236

6.55210.437

6.6213.662

6.65216.911

6.7220.185

6.75223.484

6.8226.807

6.85230.155

6.9233.527

6.95236.924

7240.345

7.05243.791

7.1247.261

7.15250.756

7.2254.275

7.25257.819

7.3261.387

7.35264.980

7.4268.598

7.45272.240

List1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

as [s]

Vzdlenost [m]


List2

List3

Shrnut Pi stejnomrn zrychlenm pmoarm pohybu se rychlost mn pmo mrn s asem. Zrychlen je vektorov veliina. Pi nerovnomrnm pohybu se zavd prmrn rychlost. Do vzorce pro prmrnou rychlost NEL- ZE dosadit okamitou, nebo ta se bhem pohybu tlesa me mnit. Pi rovnomrnm pmoarm pohybu jsou okamit a prmrn rychlost shodn. Drhu pi rovnomrn zrychlenm pohybu lze vypotat dle vzorce :

nerovnoměrný přímočarý pohyb

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