The coordinates of a particle in the metric xy-plane are differentiable functions of time t with startfraction dx over dt endfraction equalsnegative 6 startfraction m over sec endfraction and startfraction dy over dt endfraction equalsnegative 4 startfraction m over sec endfraction . how fast is the particle's distance from the origin changing as it passes through the point (12,5)?

Explanation:

It is given that,

The coordinates of a particle in the metric xy-plane are differentiable functions of time t are given by :

Let D is the distance from the origin. It is given by :

Differentiate above equation wrt t as:

.............(1)

The points are given as, (12,5). Calculating D from these points as :

Put all values in equation (1) as :

So, the particle is moving away from the origin at the rate of 7.076 m/s. Hence, this is the required solution.

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