Is Constant Acceleration Possible in Elliptical Motion?

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Constant acceleration in elliptical motion is a nuanced topic, as it can occur under specific conditions. While constant acceleration typically leads to circular motion, elliptical paths can also result from constant acceleration if the speed varies. The key factor is that acceleration must be perpendicular to the velocity vector for circular motion, but this is not the sole outcome. Thus, elliptical motion can indeed involve constant acceleration, challenging the initial assumption that it only applies to circular paths. Understanding these dynamics is crucial for accurately describing motion in physics.
SprucerMoose
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G'day all,
I was doing some maths homework and found the acceleration of a particle moving in an ellipse to be constant. Is this correct?

I would have thought that a constant acceleration would give a circle.
 
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That would only be correct in certain special cases (and the particle speed would not be constant). Your intuition was somewhat correct - a constant (magnitude) of acceleration perpendicular to the velocity vector of an object will lead to a circle, but a circular path isn't the only possibility with constant acceleration.
 
Thanks
 

Thread 'Mousetrap Car Energy efficiency'

For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...
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