A point on a rolling wheel of radius 2 traces x = 2(t - sin t), y = 2(1 - cos t)…

Step 1. The slope. $\dfrac{dy}{dx} = \dfrac{2\sin t}{2(1 - \cos t)} = \dfrac{\sin t}{1 - \cos t}$. At $t = \dfrac{\pi}{2}$ it is $1$.

Step 2. Differentiate with respect to $t$. $\dfrac{d}{dt}\dfrac{\sin t}{1 - \cos t} = \dfrac{\cos t(1 - \cos t) - \sin^2 t}{(1 - \cos t)^2} = \dfrac{\cos t - 1}{(1 - \cos t)^2} = -\dfrac{1}{1 - \cos t}$.

Step 3. Divide by $\dfrac{dx}{dt}$. $\dfrac{d^2y}{dx^2} = -\dfrac{1}{1 - \cos t} \times \dfrac{1}{2(1 - \cos t)} = -\dfrac{1}{2(1 - \cos t)^2}$.

Step 4. Put in $t = \dfrac{\pi}{2}$. $\cos t = 0$, so $\dfrac{d^2y}{dx^2} = -\dfrac{1}{2} = -0.5$.