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**Derive the expressions for velocity and acceleration in polar coordinates (that is, in terms of the unit vectors \(\hat{i}_r\) and \(\hat{i}_\theta\)).**

This involves using the polar coordinate system where positions are described by the radial distance \(r\) from the origin and the angle \(\theta\) from a reference direction. The unit vectors \(\hat{i}_r\) and \(\hat{i}_\theta\) are used to express directions in this coordinate system. To derive velocity and acceleration in these terms, consider the changes in \(r\) and \(\theta\) over time.

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