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wasizaamm43

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Suppose an object is moving along a straight line with position given by x= t^2- 8t where x is the directed distance in meters from some fixed point and t is the time in seconds.  At t= 4 seconds its speed is 0.  Is it "at rest"?  Is it "in equilibrium"?

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I am wondering if you are not confusing "equilibrium" with "stable equlibrium".

First imagine a ball rolling up a hill.  If it does not have enough kinetic energy to get to the top of the hill, it will slow to a stop, then roll back down the hill.  At the instant it stops, it is momentarily "at rest" but it is not "at equilibrium" because there is a net downward force.

Second imagine a ball sitting in a valley between two hills.  There is no net force because the downward force of gravity is offset by the upward force of the ground on the ball.  The ball is "at rest" and "at equilibrium".  If it were disturbed slightly, so that it moved a bit, it would roll back to the bottom.  That is a "stable equilibrium".

Finally imagine a ball sitting at the top of a smooth hill.  Again the only forces on the ball are gravity downward and the ground upward so there is no net force so the ball is "at rest" and "at equilibrium".  If it were disturbed slightly, so that it moved a bit, it would roll to the bottom of the hill.  That is an "unstable equilibrium".

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21 minutes ago, Country Boy said:

I am wondering if you are not confusing "equilibrium" with "stable equlibrium".

First imagine a ball rolling up a hill.  If it does not have enough kinetic energy to get to the top of the hill, it will slow to a stop, then roll back down the hill.  At the instant it stops, it is momentarily "at rest" but it is not "at equilibrium" because there is a net downward force.

Second imagine a ball sitting in a valley between two hills.  There is no net force because the downward force of gravity is offset by the upward force of the ground on the ball.  The ball is "at rest" and "at equilibrium".  If it were disturbed slightly, so that it moved a bit, it would roll back to the bottom.  That is a "stable equilibrium".

Finally imagine a ball sitting at the top of a smooth hill.  Again the only forces on the ball are gravity downward and the ground upward so there is no net force so the ball is "at rest" and "at equilibrium".  If it were disturbed slightly, so that it moved a bit, it would roll to the bottom of the hill.  That is an "unstable equilibrium".

I think you are kicking a dead donkey.

Though you are working very hard,

The OP hasn't been back since the day he joined and posted.

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