Ncert Exercises & Solutions

4.16. A cyclist starts from center O of a circular park of radius 1 km and moves along the path OPRQO as shown in the figure. If he maintains a constant speed of 10 m/s, what is his acceleration at point R in magnitude and direction?

Hint: In a uniform circular motion there is only centripetal acceleration.

Step 1: Find acceleration at point R.

As shown in the adjacent figure. The cyclist covers the path of OPRQO. As we know whenever an object performing the circular motion, acceleration is called centripetal acceleration and is always directed towards the center.

Hence, acceleration at R is $a = \frac{v^{2}}{r}$

$\Rightarrow a = \frac{(10)^{2}}{1 km} = \frac{100}{10^{3}} = 0 .1 m / s^{2} along RO$

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