One particle whose mass is defined by m is moving along a certain line in the...

One particle whose mass is defined by m is moving along a certain line in the region x>0 is subjected to a conservative net force given by the following equation: F(x)= F₀x eˣ^²/²ᴸ^²

The constants F and L are both positive real quantities with appropriate physical dimensions.

Find the formula for the corresponding U(x), with the given assumption that the limₓ↠∞U(x)=0.

Secondly, we know that the particle is launched from an initial location x₀>>>L towards x=0. (the >>> mean that its a lot larger) What is the smallest possible speed by which it is launched that still guarantees that the particle experiences maximum possible acceleration magnitude during the motion? So, acceleration of the particle =? when its speed is 1/2 its launching speed?

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genius_generous answered 1 year ago

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