Scalar Diagram (involving distances only):

math expression

We can see that:

math expression

Vector Diagram (involving velocities):

math expression

[See the section on Vector concepts for more on vectors and scalars.]

We are also given that:

math expression

Since we need math expression, we use:

math expression

Because

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we have:

math expression

So

math expression

We want to know the rate of change of q when x = 10 m, so

math expression