A classical mechanics problem by Shreyas Ravishankar
Classical Mechanics
Level
3
A point moving in the positive direction of the x axis varies as v= (a^1)*(x^0.5). where a is a positive constant. Assuming that at t=0 the particle was at x=0. find the time dependence of velocity of the particle .
does not depend on a
a^2t/2
a^2t^2/4
a^3t/9
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1 solution
Siendo la velocidad v=(a^1) (x^0.5) Y sabemos que la velocidad es la derivada de la posición con respecto al tiempo v=dx/dt=(a^1) (x^0.5) Despejamos la parte en x: dx/(x^0.5)=(a^1) dt Integrando a ambos lados llegamos a: 2 (x^0.5)=a t Y despejando la x: x=(0.5 a t)^2 Sustituyendo este valor de x en función de t en la fórmula de la velocidad que nos dan: v=0.5 a^2*t