A bus is moving with a speed of $10 \mathrm{~ms}^{-1}$ on a straight road. A scooterist wishes to overtake…

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?
  1. $20 \mathrm{~ms}^{-1}$
  2. $40 \mathrm{~ms}^{-1}$
  3. $25 \mathrm{~ms}^{-1}$
  4. $10 \mathrm{~ms}^{-1}$

Solution

Let $y$ be the relative velocity of scooter(s) w.r.t. bus $(B)$, then $\begin{aligned} \therefore \quad v_S & =\mathrm{v}+\mathrm{v}_{\mathrm{B}} \quad \ldots (i) \\ \text { Relative velocity } & =\text { displacement } / \text { time } \\ & =\frac{1000}{100}=10 \mathrm{~ms}^{-1} \end{aligned}$ Now, substituting the value of in Eq. (i), we get $\mathrm{v}_{\mathrm{S}}=10+10=20 \mathrm{~ms}^{-1}$

Asked in: NEET 2009 (Screening)

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