- The velocity of a particle moving in the positive direction of the \(x\) axis varies as \(v=\alpha \sqrt { x }\), where \(\alpha\) is a positive constant. Assuming that at the moment \(t=0\) the particle was located at the point \(x=0\), find the time dependence of the velocity and acceleration of the particle.

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proof problemsin physics in the community. Similar versions of the exercise shall be coming soon.

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TopNewest\[v = \alpha\sqrt{x} \\ \frac{dx}{\sqrt{x}} = \alpha dt \\ \int_{0}^{x}{\frac{dx}{\sqrt{x}}} = \int_{0}^{t}{\alpha dt} \\ 2\sqrt{x} = \alpha t \\ \text{This gives } \\ \boxed{v = \dfrac{{\alpha}^2}{2}t} \\ \boxed{a = \dfrac{{\alpha}^2}{2}} \] – Rajdeep Dhingra · 10 months, 1 week ago

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I suggest to keep more difficult problems. \(\ddot \smile\) – Rajdeep Dhingra · 10 months, 1 week ago

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