a
\(\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{\rm{onstant}}\,{\rm{power}}\,{\rm{acting}}\,{\rm{on}}\,{\rm{the}}\,\\
particle\,of\,mass\,m\,is\,k\,watt.\\
or\,p = k\\
\,\,\,\,\,\,\,\,\,\frac{{dW}}{{dt}} = k\,;\,\,\,dW = kdt\\
Integrating\,both\,sides,\,\int\limits_0^W {dW}  = \int\limits_0^t {k\,dt} \\
 \Rightarrow \,W = kt\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\
{\rm{Using}}\,work\,energy\,theorem,\,
\end{array}\)

\(\begin{array}{l}
W = \frac{1}{2}m{v^2} - \frac{1}{2}m{\left( 0 \right)^2}\\
kt = \frac{1}{2}m{v^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {{\rm{Using}}\,equation\left( i \right)} \right]\\
v = \sqrt {\frac{{2kt}}{m}} \\
Acceleration\,of\,the\,particle,\,a = \frac{{dv}}{{dt}}
\end{array}\)

\(\begin{array}{l}
\,\,\,\,\,\,\,a = \frac{1}{2}\sqrt {\frac{{2k}}{m}} \frac{1}{{\sqrt t }} = \sqrt {\frac{k}{{2mt}}} \\
Force\,on\,the\,particle,\\
\,F = ma = \sqrt {\frac{{mk}}{{2t}}}  = \sqrt {\frac{{mk}}{2}} \,{t^{ - 1/2}}
\end{array}\)