Question

A bus is moving with a speed of $10$ $m{s}^{-1}$ on a straight road. A scooterist wishes to overtake the bus in $100$s. If the bus in at a distance of $1$ km from the scooterist, with what speed should the scooterist chase the bus?

• A. $40m{s}^{-1}$
• B. $25m{s}^{-1}$
• C. $10m{s}^{-1}$
• D. $20m{s}^{-1}$

Answer 1

The correct option is D $20m{s}^{-1}$

Time$\left(t\right)=100s,$

distance$\left(s\right)=1km$ =$1000mVb$ = $10\frac{m}{s}$ (relative speed with respect to the bus)

Velocity$\left(V\right)=\frac{distance}{time}$= $\frac{1000}{100}$

= $10\frac{m}{s}$

$Vs$= velocity of scooter, $Vb$ = velocity of bus

$V=Vs-Vb$ (both bus scooter are moving in the same direction)

$10=Vs-10$

$10+10=Vs$

$20=Vs$

$Vs=20\frac{m}{s}$ The velocity with which scooterist should chase the bus is $20\frac{m}{s}.$