An athelete completes one round of a circular track of radius $R$ in $40 \mathrm{~s}$. What will be his…

An athelete completes one round of a circular track of radius $R$ in $40 \mathrm{~s}$. What will be his displacement at the end of $2 \min 20 \mathrm{~s}$ ?
  1. $7 R$
  2. $2 R$
  3. $2 \pi R$
  4. $7 \pi R$

Solution

The time $=2 \min 20 \mathrm{~s}$ $=2 \min +20 \mathrm{~s}$ $=2 \times 60 \mathrm{~s}+20 \mathrm{~s}=140 \mathrm{~s}$
In $40 \mathrm{~s}$ athelete completes $=1$ round In $140 \mathrm{~s}$ athelete will completes $=\frac{140}{40} \text { round }$ $=\frac{120}{40}+\frac{20}{40}$ $=3+\frac{1}{2}$ round The displacement in 3 round $=0$ So displacement in $\frac{1}{2}$ round $=A B=2 R$

Asked in: AP EAMCET 2010

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