oppgaven;
Show that if the dot product of the velocity and acceleration of a moving particle is positive (or negative), then the speed of the particle is increasing (or decreasing).
Calculus/vektor
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CharlieEppes
- Cantor
- Posts: 141
- Joined: 01/10-2014 17:26
heisann, jeg sliter litt med sånne 'vis at' oppgaver. Er ikke helt sikker på når jeg faktisk har vist påstanden eller hva. Hadde satt stor pris på litt hjelp til den medfølgene oppgaven, + litt tips om hvordan man skal "angripe" slike oppgaver (hvordan man bør tenke) osv...
oppgaven;
Show that if the dot product of the velocity and acceleration of a moving particle is positive (or negative), then the speed of the particle is increasing (or decreasing).
oppgaven;
Show that if the dot product of the velocity and acceleration of a moving particle is positive (or negative), then the speed of the particle is increasing (or decreasing).
"Insanity; doing the same thing over and over again, and expecting different results." -Albert Einstein
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CharlieEppes
- Cantor
- Posts: 141
- Joined: 01/10-2014 17:26
[*]v er velocity
a er acceleration
Anta 0< a · v = |v||a|*cosΩ, der Ω er vinkelen mellom a,v.
= > 0 < cosΩ ≤ 1
=> 0 < a · v = |a||v|
=> 0 < |a| = (a · v)/|v| = d/dt( |v|)
=> 0 < d/dt (|v|)
er dette bra nok?
a er acceleration
Anta 0< a · v = |v||a|*cosΩ, der Ω er vinkelen mellom a,v.
= > 0 < cosΩ ≤ 1
=> 0 < a · v = |a||v|
=> 0 < |a| = (a · v)/|v| = d/dt( |v|)
=> 0 < d/dt (|v|)
er dette bra nok?
"Insanity; doing the same thing over and over again, and expecting different results." -Albert Einstein