# NCERT Class 11 Physics Solutions: Chapter 4 – Motion in a Plane Part 4

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Question 4.9:

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. 4.9. If the round trip takes 10 min, what is the

(a) Net displacement,

(b) Average velocity, and

(c) Average speed of the cyclist?

Fig. 4.9

(a) Net displacement:

Displacement is given by the minimum distance between the initial and final positions of a body. In the given case, the cyclist comes to the starting point after cycling for 10 minutes. Hence, his net displacement is zero.

(b) Average velocity:

Average velocity is given by the relation:

Average velocity

Since the net displacement of the cyclist is zero, his average velocity will also be zero.

(c) Average speed of the cyclist:

Average speed

Total path length

Time taken = 10 min

Question 4.10:

On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. starting from a given turn; specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

The path followed by the motorist is a regular hexagon with side 500 m, as shown in the

Given figure:

Let the motorist start from point P.

The motorist takes the third turn at S.

Magnitude of displacement

Total path length

The motorist takes the sixth turn at point P, which is the starting point.

Magnitude of displacement

Total path length

The motorist takes the eight turn at point R.

Motorist takes the eight turn at point R

Therefore, the magnitude of displacement is 866.03 m at an angle of 30° with PR.

Total path length = Circumference of the hexagon + PQ + QR

The magnitude of displacement and the total path length corresponding to the required turns is shown in the given table:

 Turn Magnitude of displacement (m) Total path length (m) Third 1000 1500 Sixth 0 3000 Eighth 866; 30° 4000