# A bus is moving with a speed of $10 m/s$ on a straight 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?

$(a)\;40\; m/s \quad (b)\;25 \;m/s \quad (c)\;10 \;m/s \quad(d)\;20\; m/s$

Let $V_{SB}$=relative velocity of scooterist with respect to bus
$V_S$=Velocity of Scooterist
$V_B$=Velocity of Bus
$V_{SB}=V_S-V_B=>V_S=V_{SB}+V_B$
Since the scooterist has to cross the bus $1km$ distance in $100$ second.
$V_{SB}=\large\frac{1000\;m }{100\;s}$$=10 m/s$
Therefore $V_S=10+10=20 m/s$
Hence d is the correct answer

edited Jan 26, 2014 by meena.p