## Question

A cyclist starts from the centre *O* of a circular track of radius *r* = 1 km, reaches the edge *P* of the track and then cycles along circumference and stops at point *Q*. if the total time take is 10 min, what is the average velocity of the cyclist?

### Solution

6 km h^{–1}

The displacement of the cyclist in moving from *P* to *Q* along the circumference = shortest distance between *P* and *Q* = straight line distance *PQ* in the direction from *P* to *Q*. The net displacement in moving from *O* to *P* and then from *P* to *Q* = resultant of vector displacement *OP* and *PQ*. From the triangle law of vector addition, the magnitude of the net displacement = *OQ* = 1 km. Now, the time take = 10 min Therefore, average velocity is 1 km/ = 6 km h^{–1}.

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