###### NCERT Solution: Motion

**NCERT Exercise**

**An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?**

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

= 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

= 200 m