A bus is moving with a speed of $10\; ms^{-1}$ on a striaght road. A scooterist wishes to overtake the bus in $100\,s$ . If the bus is at a distance of $1\,km$ from the scooterist, with what speed should the scooterist chase the bus ?.........$m/s$
✓
Answer
d
$\begin{array}{l}
Let\,\,{v_s}\,\,be\,the\,velocity\,of\,the\,scooter,\,the\,{\rm{distance}}\,between\,the\\
scooter\,and\,the\,bus\, = 1000\,m,\\
The\,velocity\,of\,the\,bus\, = 10\,m{s^{ - 1}}\\
Time\,taken\,to\,overtake\, = \,100\,s\\
{\rm{Relative}}\,velocity\,of\,the\,scooter\,with\,respect\,to\,the\,\\
bus = \left( {{v_s} - 10} \right)\\
\therefore \frac{{1000}}{{\left( {{v_s} - 10} \right)}} = 100\,s \Rightarrow {v_s} = 20\,m{s^{ - 1}}
\end{array}$
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