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• Notes

$\begin{array}{l}{\text { A bird is flying due east. Its distance from a tall building is given by } x(t)=28 m+(12.4 \mathrm{m} / \mathrm{s}) \mathrm{t}-\left(0.0450 \mathrm{m} / \mathrm{s}^{\wedge} \mathrm{J}\right) \mathrm{t}^{\wedge} 3} \\ {\text { What is the instantaneous velocity of the bird when } \mathrm{t}=8 \mathrm{s} ?}\end{array}$

$V_{x}(t)=\frac{d x}{d t}=\frac{d\left(28+12.4 t-0.045 t^{3}\right)}{d t}$

$\rightarrow v_{x}(t)=\frac{d x}{d t}=12.4-3(0.045) t^{2}$

$=12.4-(0.135) t^{2}$

$a t \ t=8 s$

$V_x(8)=12.4-(0.135)(8)^{2}=3.76 \mathrm{m} / \mathrm{s}$

$\begin{array}{l}{\text { A race car starts from rest and travels east along attraight and level track. For the }} \\ {\text { first } 5.0 \text { s of the car's motion, the eastward component of the car's velocity is given by }} \\ {\mathrm{V} x(t)=(0.86) \mathrm{t}^{2} \text { . What is the acceleration of the car when } \mathrm{V} x=16 \mathrm{m} / \mathrm{s} \text { ? }}\end{array}$

$a_{x}(t)=\frac{d v_{x}}{d t}=\frac{d((0.86)) t^{2}}{d t}$

$a_{x}(t)=\frac{d v_{x}}{d t}=(1.72) t$

$\text { when } V_{x}=16 \mathrm{m} / \mathrm{s} \rightarrow 16=(0.86) t^{2} \rightarrow \mathrm{t}=4.313s$

$\rightarrow a _x=(1.72)(4.313)=7.42 \mathrm{m} / \mathrm{s}^{2}$