Answer
$$\dfrac{1}{5}$$
Work Step by Step
The vector formula for curvature can be written as: $k=\dfrac{|v \times a(t)|}{|v^3|} ...(1)$
But $v \times a(t)=25 k$
So, $|v \times a(t)|=25 $
and $|v|=\sqrt {(3)^2+(4)^2}=5$
Thus, equation (1) becomes: $$k=\dfrac{|v \times a(t)|}{|v^3|}=\dfrac{25}{(5)^3}=\dfrac{1}{125}=\dfrac{1}{5}$$
