A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. 4.21. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist?

Question

A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. 4.21. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist?

Philoid · Accepted Answer

(a) Displacement is given by the change in position. In the given case, the initial position is also the final position i.e., there is no change in position. So, net displacement is zero.

(b) Average velocity is the ratio of net displacement to the time taken.

i.e.,

Since net displacement is zero, average velocity is also zero.

(c) Average speed is the ratio of total path length to the time taken.

i.e.,

Here, total path length = OP+PQ+QO

⇒ total path length = r + + r

(∵ Circumference of a circle = 2πr)

⇒ total path length = r×(2+)

⇒ total path length = 1km× (2+1.57)

So, total path length = 3.57km

Also, time taken = 10min (given)

Hence, average speed =

⇒ average speed =

⇒ average speed = 21.42 km/hr