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A bird flies with a velocity ( $\mathrm{t}-2) \mathrm{ms}^{-1}$ along a straight line, where $t$ is the time in seconds. The distance cevered by it in a time of 4 seconds is
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The correct answer is:
$4 \mathrm{~m}$
Velocity of bird flies, $\mathrm{v}=|\mathrm{t}-2| \mathrm{m} / \mathrm{s}$ at $\mathrm{t}=0 \mathrm{~s}, \mathrm{v}=2 \mathrm{~m} / \mathrm{s}$
at $\mathrm{t}=2 \mathrm{~s}, \mathrm{v}=0 \mathrm{~m} / \mathrm{s}$
at $\mathrm{t}=4 \mathrm{~s}, \mathrm{v}=2 \mathrm{~m} / \mathrm{s}$
Distance between $\mathrm{t}=0 \mathrm{~s} \mathrm{t} \mathrm{t}_0-\mathrm{t}=2 \mathrm{~s}$
$$
\begin{aligned}
& \mathrm{S}_1=\mathrm{v} \Delta \mathrm{t}+\frac{1}{2} \mathrm{a}_1(\Delta \mathrm{t})^2 \\
& \mathrm{a}_1=\frac{0-2}{2-0}=-1 \mathrm{~m} / \mathrm{s}^2 \\
& =2 \times 2+\frac{1}{2} \times(-1) \times 2^2 \\
& =4-2 \\
& =2 \mathrm{~m}
\end{aligned}
$$
Distance between $\mathrm{t}=2 \mathrm{~s}$ to $\mathrm{t}=4 \mathrm{~s}$
$$
\begin{aligned}
& \mathrm{s}_2=\mathrm{v}(\Delta \mathrm{t})+\frac{1}{2} \mathrm{a}_2(\Delta \mathrm{t})^2 \\
& \mathrm{a}_2=\frac{2-0}{4-2}=1 \mathrm{~m} / \mathrm{s}^2 \\
& =0 \times 4+\frac{1}{2} \times 1 \times 2^2 \\
& =2
\end{aligned}
$$
$\begin{aligned} & \text { Total distance }=s_1+s_2 \\ & =2+2=4 m\end{aligned}$
at $\mathrm{t}=2 \mathrm{~s}, \mathrm{v}=0 \mathrm{~m} / \mathrm{s}$
at $\mathrm{t}=4 \mathrm{~s}, \mathrm{v}=2 \mathrm{~m} / \mathrm{s}$
Distance between $\mathrm{t}=0 \mathrm{~s} \mathrm{t} \mathrm{t}_0-\mathrm{t}=2 \mathrm{~s}$
$$
\begin{aligned}
& \mathrm{S}_1=\mathrm{v} \Delta \mathrm{t}+\frac{1}{2} \mathrm{a}_1(\Delta \mathrm{t})^2 \\
& \mathrm{a}_1=\frac{0-2}{2-0}=-1 \mathrm{~m} / \mathrm{s}^2 \\
& =2 \times 2+\frac{1}{2} \times(-1) \times 2^2 \\
& =4-2 \\
& =2 \mathrm{~m}
\end{aligned}
$$
Distance between $\mathrm{t}=2 \mathrm{~s}$ to $\mathrm{t}=4 \mathrm{~s}$
$$
\begin{aligned}
& \mathrm{s}_2=\mathrm{v}(\Delta \mathrm{t})+\frac{1}{2} \mathrm{a}_2(\Delta \mathrm{t})^2 \\
& \mathrm{a}_2=\frac{2-0}{4-2}=1 \mathrm{~m} / \mathrm{s}^2 \\
& =0 \times 4+\frac{1}{2} \times 1 \times 2^2 \\
& =2
\end{aligned}
$$
$\begin{aligned} & \text { Total distance }=s_1+s_2 \\ & =2+2=4 m\end{aligned}$
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