# A body of mass m moving along a straight line covers half the distance with a speed of 2ms^-1. The remaining half of the distance is covered in two equal time intervals with a speed of 3 ms^-1 and 5 ms^-1 respectively. The average speed of the particle for the entire journey is (A) 3/8 ms^-1 (B) 8/3 ms^-1 (C) 4/3 ms^-1 (D) 16/3 ms^-1

Let the total distance travelled by the body = 2S

If t1 is the time taken by the body to travel first half of the distance, then

t1 = S/2

For remaining half journey, let t2 be the time taken by the body for each time interval

S = 3t2 + 5t2 = 8t2

Hence, average speed = (total distance travelled)/ (total time taken)

= 2S/(t1 + 2t2)

= 2S/(S/2 + S/4)

On calculating, we get,

= 8/3 ms-1

Therefore, the average speed of the particle for the entire journey is 8/3 ms-1

So, the correct option is (B)