parametrization of a moving wheel

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Attempt:

Given, radius of wheel $0.5 m$

Total distance travelled by the point during first revolution = circumference of the wheel

therefore, distance travelled by the point $2 \pi r$

where r is the radius of the wheel

distance travelled by the point $2 \cdot 3.14 \cdot 0.5 = 3.14 m$

Now, a circle can be defined as the locus of the all points on it that satisfies the equations,

$x = r cos(t), y = rsin(t)$

where x, y are the coordinates of any point on the circle, r is the radius of the circle and t is the parameter - the angle subtended by the point at the circle's center

so the parametrization of the path would be

$x = 0.5cos(t), y = 0.5sin(t)$

Is it right?

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That parametrization is with respect to the midpoint of the wheel. But note that the midpoint is moving as well! You'll need to account for that movement, too, see https://en.wikipedia.org/wiki/Cycloid.