$\overrightarrow{\mathrm{P}}=\cos (\mathrm{kt}) \hat{\mathrm{i}}-\sin (\mathrm{kt}) \hat{\mathrm{j}} ;|\overrightarrow{\mathrm{P}}|=1$
$\because \overrightarrow{\mathrm{P}}=\mathrm{m} \overrightarrow{\mathrm{v}}$
$\therefore \hat{\mathrm{P}}=\hat{\mathrm{v}}$
$\Rightarrow \hat{\mathrm{v}}=\cos (\mathrm{kt}) \hat{\mathrm{i}}-\sin (\mathrm{kt}) \hat{\mathrm{j}}$
$\hat{\mathrm{a}}=\frac{-\mathrm{k} \sin (\mathrm{kt}) \hat{\mathrm{i}}-\mathrm{k} \cos (\mathrm{kt}) \hat{\mathrm{j}}}{\mathrm{k}}$
$\Rightarrow \hat{\mathrm{a}}=-\sin k t \hat{\mathrm{i}}-\cos k \hat{\mathrm{t}}$
$\because \hat{\mathrm{F}}=\hat{\mathrm{a}}=-\sin \mathrm{kt} \hat{\mathrm{i}}-\cos k t \hat{\mathrm{j}}$
$\cos \theta=\frac{\hat{\mathrm{F}} \cdot \hat{\mathrm{P}}}{|\hat{\mathrm{F}}| \hat{\mathrm{P}} \mid}=-\frac{\sin k t \cos \mathrm{t}+\sin k t \cos \mathrm{t}}{1 \times 1}=0$
$\Rightarrow \theta=\frac{\pi}{2}$