question_answer

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 is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus? [AIPMT (S) 2009]

A) \[20\,m{{s}^{-1}}\]

B) \[40\,m{{s}^{-1}}\]

C) \[25\,m{{s}^{-1}}\]

D) \[10\,m{{s}^{-1}}\]

Correct Answer: A

Solution :

Let v be the relative velocity of scooter(s) w.r.t. bus (B), then

\[\to \]   \[{{v}_{s}}=v+{{v}_{B}}\]                             (i)

Relative velocity = displacement/time

\[=\frac{1000}{100}=10\,m{{s}^{-1}}\]

Now, substituting the value of v in Eq. (i), we

Get       \[{{v}_{s}}=10+10=20\,m{{s}^{-1}}\]