# How do you find the velocity of a particle that moves along a line?

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To find the velocity of a particle that moves along a line, you need to differentiate its position function with respect to time. Mathematically, if ( s(t) ) represents the position function of the particle at time ( t ), then the velocity function, denoted by ( v(t) ), is found by taking the derivative of ( s(t) ) with respect to time, ( t ).

In symbols, ( v(t) = \frac{ds}{dt} ).

Once you have the velocity function ( v(t) ), you can evaluate it at specific times to find the instantaneous velocity of the particle at those times. Alternatively, if you want to find the average velocity of the particle over a certain time interval, you can integrate the velocity function over that interval and divide by the length of the interval.

This process applies to particles moving along a straight line in one-dimensional motion. If the motion is in two or three dimensions, then you would have separate position functions for each dimension and find the velocity in each dimension accordingly.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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