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A bus is moving with a speed of $10 \mathrm{~ms}^{-1}$ on a straight road. A scooterist wishes to overtake the bus in $100 \mathrm{~s}$. If the bus is at a distance of $1 \mathrm{~km}$ from the scooterist, with what speed should the scooterist chase the bus?
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Verified Answer
The correct answer is:
$20 \mathrm{~ms}^{-1}$
Let $y$ be the relative velocity of scooter(s) w.r.t. bus $(B)$, then
$$
\begin{aligned}
\therefore \quad v_S & =\mathrm{v}+\mathrm{v}_{\mathrm{B}} \\
\text { Relative velocity } & =\text { displacement } / \text { time } \\
& =\frac{1000}{100}=10 \mathrm{~ms}^{-1}
\end{aligned}
$$
Now, substituting the value of in Eq. (i), we get
$$
\mathrm{v}_{\mathrm{S}}=10+10=20 \mathrm{~ms}^{-1}
$$
$$
\begin{aligned}
\therefore \quad v_S & =\mathrm{v}+\mathrm{v}_{\mathrm{B}} \\
\text { Relative velocity } & =\text { displacement } / \text { time } \\
& =\frac{1000}{100}=10 \mathrm{~ms}^{-1}
\end{aligned}
$$
Now, substituting the value of in Eq. (i), we get
$$
\mathrm{v}_{\mathrm{S}}=10+10=20 \mathrm{~ms}^{-1}
$$
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