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Hi, I need help with this problem:

I guess this one:

##v= \frac {ds}{dt}##

If the object moves from A to B in the least time possible, that means that ##\Delta t## tends to ##0##. To find the maximum speed I need to find the moment when the object travels more dinstance in the least time. That would be the derivative of the distance ##L## with respect to ##t##, so ##lim_{\Delta t\to 0} \frac{\Delta L} {\Delta t} = \frac {dL} {dt}##. Am I right? The problem is that I don't know hot to find the maximum speed necessary. How do I find the maximum speed?

**1. The problem statement, all variables and given/known data***Condition: an object has to move from point A to point B in the least time possible. The distance between the points is L. The object can accelerate (decelerate) with a fixed acceleration ##a## or move with a constant speed.**What maximum speed does this object have to reach to satisfy the condition?***2. Relevant equations**I guess this one:

##v= \frac {ds}{dt}##

**3. The attempt at a solution**If the object moves from A to B in the least time possible, that means that ##\Delta t## tends to ##0##. To find the maximum speed I need to find the moment when the object travels more dinstance in the least time. That would be the derivative of the distance ##L## with respect to ##t##, so ##lim_{\Delta t\to 0} \frac{\Delta L} {\Delta t} = \frac {dL} {dt}##. Am I right? The problem is that I don't know hot to find the maximum speed necessary. How do I find the maximum speed?

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