Answer:
Let the bill board be taken as the origin. Let t be the required time. Let P represent the position where the police officer reaches the motorist.
For the motorist. (It is a case of uniform motion). \[v=45km{{h}^{-1}}\] \[\therefore S=45t\,\,km\] … (1) For the police officer. (It is a case of accelerated motion) \[a=10km{{h}^{-2}}\] \[S=ut+\frac{1}{2}a{{t}^{2}}\] \[S=0+\frac{1}{2}10\times {{t}^{2}}=5{{t}^{2}}km\] …. (2) Comparing (2) and (1), we get \[5{{t}^{2}}=45t\,\,or\,\,t=9\,\,hours.\]
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