A particle starts from rest at x = 0 and moves along the x-axis such that its velocity is given by v = k x , where k is a positive constant. Which of the following correctly describes its position x

Question

A particle starts from rest at x = 0 and moves along the x-axis such that its velocity is given by v = k x ​ , where k is a positive constant. Which of the following correctly describes its position x as a function of time t ?

TestHub · Accepted Answer

Given v = d t d x ​ = k x ​ . Separate variables: x ​ d x ​ = k d t . Integrate both sides from x = 0 to x and t = 0 to t : ∫ 0 x ​ x − 1/2 d x = ∫ 0 t ​ k d t . [ 2 x ​ ] 0 x ​ = [ k t ] 0 t ​ . This simplifies to 2 x ​ = k t . Squaring both sides gives x = 4 k 2 t 2 ​ .

Physics - Kinematics Question with Solution | TestHub

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