Question

An athlete complete ane round of a circular track
of diameter 200m in 40 seconds. What wile
be the distance covered and the displacement
at the end of 2 m 20s (140 s)?​

Answer 1

Question: An athelete completes 1round of a circular track of diameter 200m in 40 seconds. What will be the distance covered and the displacement at the end of 2 mins 20 secs?

Answer :

We know that, Displacement is the shortest distance between two points.

Now,

Circumference = 2 π r

Diameter = 200 m

Therefore, Radius = 100 m

Thus,

Distance covered in a round i.e 40 seconds =

$\tt {2 \times \frac{22}{7} \times 100}$ $\tt {= 6.28 \times 100}$$\tt {= 6.28 \times 100}$

This is the distance covered in 40 sec.

Thus, Distance covered in 1 sec,

$\tt{= \frac{628}{40}}$$\tt{ = 15.7m}$

As per the question,

We have to find the distance covered at the end of 2 min. 20 secs.

2 min 20 sec = 140 sec.

Hence, Distance covered in 140 sec

= 15.7 × 140

= 2198 metres.

Distance covered in 140 sec is 2198 metres.

We know that, Displacement is the shortest distance between two points.

Displacement of the athlete will be equal to the diameter of the circular track.

∴ Displacement of the athlete = 200 m

Final answer :

The distance covered is 2198 metres and the displacement at the end of 2 minutes 20 seconds is 200 m.

Answer 2

Diameter of circular track (D) = 200 m

Radius of circular track (r) = 200 / 2=100 m

Time taken by the athlete for one round (t) = 40 s

Distance covered by athlete in one round (s) = 2π r

= 2 × ( 22 / 7 ) × 100

Speed of the athlete (v) = Distance / Time

= (2 × 2200) / (7 × 40)

= 4400 / 7 × 40

Therefore, Distance covered in 140 s = Speed (s) × Time(t)

= 4400 / (7 × 40) × (2 × 60 + 20)

= 4400 / (7 × 40) × 140

= 4400 × 140 /7 × 40

= 2200 m

Number of round in 40 s =1 round

Number of round in 140 s =140/40

=3 1/2

After taking start from position X,the athlete will be at postion Y after 3 1/2 rounds as shown in figure

Hence, Displacement of the athlete with respect to initial position at x= xy

= Diameter of circular track

= 2200m