Question

A cyclist starts from the center O of circle of park of radius 1 km, reaches the edge P of the park, then cycles along the circumference to point Q and returns to the centre along QO as shown. If the round trip takes 10 minutes, then what is:

(a) net displacement
(b) average velocity
(c) average speed of the cyclist?

Solution

(a) The cyclist starts from O and again returns to point O. Therefore, the initial and the final point are the same. Hence, displacement of cyclist is equal to zero.
(b) Average velocity of cyclist is zero because total displacement of cyclist is zero.
(c) Total distance travelled by cyclist is,
$straight S equals OP plus PQ with overparenthesis on top plus QO$
$equals straight r plus πr over 2 plus straight r equals straight r open parentheses fraction numerator 4 plus straight pi over denominator 2 end fraction close parentheses$
∴ Average speed = $straight S over straight t equals open parentheses fraction numerator 4 plus straight pi over denominator 2 end fraction close parentheses straight r over straight t$
Here, we have
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and
Time taken for round trip, $space space space straight t equals 10 min equals 600 straight s$
∴ $Average space speed space equals space open parentheses fraction numerator 4 plus straight pi over denominator 2 end fraction close parentheses 1000 over 600$
$space space equals 5.95 space straight m divided by straight s$

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