A particle moving in the xy plane experiences a velocity dependent force F→$$=kvyi^+vxj^$$, where vx and vy are the x and y components of its velocity v→. If a→ is the acceleration of the particle, then which of the following statements is true for the particle?

Question

A particle moving in the  xy plane experiences a velocity dependent force  F→$$=kvyi^+vxj^$$, where vx  and vy are the x and y components of its velocity  v→.   If  a→ is the acceleration of the particle, then which of the following statements is true for the particle?

Infinity Learn · Accepted Answer

let mass of the particle is m then  a→$$=km$$ $$vyi^+vxj^$$  and  v→$$=vxi^+vyj^Let$$   $$km=$$α (constant)  So  α$$vy=dvxdt$$  and  α$$vx=dvydtDividing$$, $$dvxdvy=vyvx$$​⇒∫$$vxdvx=$$∫vydvy​⇒$$vx2$$−$$vy2=constant$$​​Now, v→×a→$$=vxi^+vyj^$$×$$kmvyi^+vxj^=kmvx2$$−$$vy2k^$$ $$=$$ constant

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A particle moving in the xy plane experiences a velocity dependent force F→=kvyi^+vxj^, where vx and vy are the x and y components of its velocity v→. If a→ is the acceleration of the particle, then which of the following statements is true for the particle?

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