- #1
songoku
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Homework Statement
[tex]x=\left(\begin{array}{cc}\frac{3}{5}t^2+2t\\10t^2+1\end{array}\right) , 0\leq t \leq 5 \; \text {and} \; F=\left(\begin{array}{cc}3\\1\end{array}\right)[/tex]
a. find v in vector form
b. find mass
c. when t = 5, there is addition of [tex]F=\left(\begin{array}{cc}t\\0\end{array}\right)[/tex]. Find the acceleration when t = 6
d. find v when t = 6
Homework Equations
F = ma
The Attempt at a Solution
a. [tex]v=\left(\begin{array}{cc}\frac{6}{5}t+2\\20t\end{array}\right)[/tex]b. [tex]|F|=\sqrt{3^2+1^2}=\sqrt{10}[/tex]
[tex]a=\left(\begin{array}{cc}\ 6/5 \\20\end{array}\right)[/tex]
[tex]|a|=\sqrt{\left(\frac{6}{5}\right)^2+20^2}\approx 20.04[/tex]
[tex]m=\frac{|F|}{|a|}=\frac{\sqrt{10}}{20.04}\approx 0.158\; kg[/tex]c. [tex]F \; \text{total}=\left(\begin{array}{cc}3\\1\end{array}\right)+\left(\begin{array}{cc}t\\0\end{array}\right) = \left(\begin{array}{cc}3\\1\end{array}\right)+\left(\begin{array}{cc}6\\0\end{array}\right)=\left(\begin{array}{cc}9\\1\end{array}\right)[/tex]
[tex]|F \; \text{total}|=\sqrt{9^2+1^2}=\sqrt{82}[/tex]
[tex]|a|=\frac{|F|}{m}\approx 57.31 \;ms^{-2}[/tex]d. [tex]v=\left(\begin{array}{cc}46/5\\120\end{array}\right)[/tex]
[tex]|v|=\sqrt{\left(\frac{46}{5}\right)^2+120^2}\approx 120.35 \;ms^{-1}[/tex]Do I get it right ?
Thx