Physics - Circular Motion Question with Solution | TestHub

The component of $\vec{a}$ perpendicular to $\vec{v}$ is the centripetal part: $a_c=2\mathrm{m}/{\mathrm{s}}^2$ (the $\hat{ȷ}$ component, since $\vec{v}$ is along $\hat{ı}$ ).
So $R=\frac{v^2}{a_c}$
$=\frac{4}{2}$
$=2\mathrm{m}$ (Assertion true).
The tangential component is $a_t=\frac{\vec{v}\cdot \vec{a}}{v}$
$=\frac{-2}{2}$
$=-1\mathrm{m}/{\mathrm{s}}^2$, so the speed is decreasing at $1\mathrm{m}/{\mathrm{s}}^2$ (Reason true).
The Reason, however, is not what fixes the radius, so it does not explain the Assertion.