**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.

The unit vector along r and θ in terms of cartesian coordinates is given by Where i = unit vector along x-direction j = unit vector along y-direction The position vector of the particle in polar coordinates is given by The velocity of the particle is given by But Thus The acceleration of the particle is given by But Thus

Answered: Derive the expressions for velocity and…

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Derive the expressions for velocity and acceleration in polar coordinates (that is, in terms of the unit vectors î, and io).