5.14 Related Rates
We have seen that is
the derivative of s (t) w. r. to t and can be interpreted as the velocity.
This physical interpretation can be extended further.
If (x, y) are the coordinates of a moving particle then both x and y are functions of ’ t ’.
, then, is the rate of change of x w. r. to ’ t ’ and is
the rate of change of y w. r. to ’ t’
since
both x and y are related by a function y = f (x),
are also related. If one of is known the other can be found using the relation
between these rates.
Problem of this type are known as problem of related rates.
Technique : y = f (x) where both x and y are dependent on time ' t '
Hence
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