Solution 19.5a
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(New page: <math>\begin{align} & v=\int{adt} \\ & \\ & =\int{\left( -kt \right)dt} \\ & \\ & =-\frac{k{{t}^{2}}}{2}+c \\ & \\ & t=0,\ v=20\ \Rightarrow \ c=20 \\ & \\ & v=20-\frac{k{{t}^{...)
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Revision as of 15:37, 11 October 2010
\displaystyle \begin{align} & v=\int{adt} \\ & \\ & =\int{\left( -kt \right)dt} \\ & \\ & =-\frac{k{{t}^{2}}}{2}+c \\ & \\ & t=0,\ v=20\ \Rightarrow \ c=20 \\ & \\ & v=20-\frac{k{{t}^{2}}}{2} \\ & \\ & \text{ Using}\quad t=40,\ v=5\quad \text{gives} \\ & \\ & 5=20-\frac{k\times {{40}^{2}}}{5} \\ & \\ & 320k=15 \\ & \\ & k=\frac{15}{320}=\frac{3}{64} \end{align}
