MÜ05. Mootorratta kiirendus ja kulunud aeg

Ülesanne. Mootorratas alustas liikumist paigalseisust ühtlaselt kiirenevalt ja peale 0,05 km läbimist saavutas kiiruse 90 km/h. Leida kulunud aeg ja kiirendus.

Lahendus. Esmalt paneme kirja andmed.

Antud:

s equals 0 comma 05 space k m equals 50 space m v equals 90 space fraction numerator k m over denominator h end fraction equals 25 m over s minus negative negative negative negative negative negative negative negative negative negative negative a minus ? t minus ?

Saame leida alustuseks kiirenduse ning seejärel kulunud aja:

a equals fraction numerator v squared minus v subscript 0 squared over denominator 2 s end fraction equals fraction numerator 625 begin display style m squared over s squared end style minus 0 begin display style m squared over s squared end style over denominator 2 times 50 space m end fraction equals 6 comma 25 m over s squared a equals fraction numerator v minus v subscript 0 over denominator t end fraction rightwards double arrow t equals fraction numerator v minus v subscript 0 over denominator a end fraction equals fraction numerator left parenthesis 25 minus 0 right parenthesis begin display style m over s end style over denominator 6 comma 25 begin display style m over s squared end style end fraction equals 4 space s.

Saab ka esimesena leida aja ning seejärel kiirenduse:

t equals s over v subscript k equals fraction numerator 50 space m over denominator begin display style fraction numerator left parenthesis 25 plus 0 right parenthesis begin display style m over s end style over denominator 2 end fraction end style end fraction equals 4 space s a equals fraction numerator v minus v subscript 0 over denominator t end fraction equals fraction numerator left parenthesis 25 minus 0 right parenthesis begin display style m over s end style over denominator 4 space s end fraction equals 6 comma 25 m over s squared

 

VASTUS: Mootorratta kiirendus läbitud 50 m jooksul on 6 comma 25 m over s squared ning kulunud aeg 4 space s.