Answer to Question #114407 in Differential Equations for Josh Miles

Question

The velocity of a moving vehicle is given by the equation v=(2t+3)^4 .Use the Chain Rule to determine an equation for the acceleration when a=dv/dt.

Answer 1

We will use the Chain Rule for the following functions: $v = (2t+3)^4 = f(g(t))$, where $f(t) = t^4, g(t) = 2t + 3$ .

Since $\frac{df}{dt} = 4t^3$ and $\frac{dg}{dt} = 2$ , by the chain rule, we obtain that:

$a = \frac{dv}{dt} = \frac{df}{dg} \frac{dg}{dt} = 4(2t+3)^3 \cdot 2 = 8(2t+3)^3$