find d²v/dt². v = 2t² + 8t + 15 d²v/dt² = □

Explanation:

Step1: Find first - derivative

Differentiate $v = 2t^{2}+8t + 15$ with respect to $t$. Using the power rule $\frac{d}{dt}(at^{n})=nat^{n - 1}$, we have $\frac{dv}{dt}=\frac{d}{dt}(2t^{2})+\frac{d}{dt}(8t)+\frac{d}{dt}(15)=4t + 8$.

Step2: Find second - derivative

Differentiate $\frac{dv}{dt}=4t + 8$ with respect to $t$. Again using the power rule, $\frac{d^{2}v}{dt^{2}}=\frac{d}{dt}(4t)+\frac{d}{dt}(8)=4$.

Answer:

$4$