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**Hint:**Calculate the horizontal and vertical displacements of point P. Then calculate the resultant displacement of the point P.

**Formulae used:**

The circumference \[C\] of the circle is given by

\[ \Rightarrow C = 2\pi r\] …… (1)

Here, \[r\] is the radius of the circle.

The resultant displacement \[s\] is given by

\[ \Rightarrow s = \sqrt {s_x^2 + s_y^2} \] …… (2)

Here, \[{s_x}\] is the horizontal component of displacement and \[{s_y}\] is the vertical component of displacement.

**Complete step by step answer:**

Calculate the horizontal displacement of the point P between the times \[{t_1}\] to \[{t_2}\].

The horizontal displacement \[{s_x}\] of the point P is equal to half of the circumference \[C\] of the wheel.

\[ \Rightarrow {s_x} = \dfrac{C}{2}\]

Substitute \[2\pi r\] for \[C\] in the above equation.

\[ \Rightarrow {s_x} = \dfrac{{2\pi r}}{2}\]

Substitute \[3.14\] for \[\pi \] and \[45\,{\text{cm}}\] for \[r\] in the above equation.

\[{s_x} = \dfrac{{2\left( {3.14} \right)\left( {45\,{\text{cm}}} \right)}}{2}\]

\[ \Rightarrow {s_x} = 141.3\,{\text{cm}}\]

Hence, the horizontal displacement of the point P is \[141.3\,{\text{cm}}\].

Calculate the vertical displacement of the point P between the times \[{t_1}\] to \[{t_2}\].

The vertical displacement \[{s_y}\] of the point P is equal to the diameter of the wheel which is twice the radius \[r\] of the wheel.

\[ \Rightarrow {s_y} = 2r\]

Substitute \[45\,{\text{cm}}\] for \[r\] in the above equation.

\[ \Rightarrow {s_y} = 2\left( {45\,{\text{cm}}} \right)\]

\[ \Rightarrow {s_y} = 90\,{\text{cm}}\]

Hence, the vertical displacement of the point P is \[90\,{\text{cm}}\].

Now calculate the resultant displacement \[s\] of the point P.

Substitute \[141.3\,{\text{cm}}\] for \[{s_x}\] and \[90\,{\text{cm}}\] for \[{s_y}\] in equation (2).

\[ \Rightarrow s = \sqrt {{{\left( {141.3\,{\text{cm}}} \right)}^2} + {{\left( {90\,{\text{cm}}} \right)}^2}} \]

\[ \Rightarrow s = 167.5\,{\text{cm}}\]

\[ \Rightarrow s = 168\,{\text{cm}}\]

Therefore, the displacement of the point P is \[168\,{\text{cm}}\].

**Hence, the correct option is B.**

**Note:**One may directly determine the diameter of the wheel to calculate the displacement of point P. But it is the vertical displacement and not the resultant displacement.

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