Question

In a complete circular motion, first half circle is
covered with 6 m/s. The other half circle is covered
in two equal time intervals at speed 4 m/s and
2 m/s respectively. The average speed during the
circular motion is
(1) 2 m/s
(2) 3 m/s
(3) 4 m/s
(4) 5 m/s​

Answer 1

answer : option (3) 4m/s

explanation : Let total distance covered to complete the circle is x m

first half distance is covered by speed 6 m/s and other half circle is covered in two equal time interval at speed 4m/s and 2m/s respectively.

time taken to complete half circle , t1 = (x/2)/6 = (x/12) s

now rest (x/2) m covered by 4m/s and 2m/s in equal time interval.

so, (x/2) = 4t + 2t

or, t = (x/12)s

so, time taken to complete second half , t2 = 2t = (x/6)s

now, average speed = total distance/total time

= x/(x/12 + x/6)

= x/(3x/12)

= 12x/3x = 4

hence, average speed = 4m/s

2nd method :

using formula,

v = $\frac{2v_1(v_2+v_3)}{2v_1+v_2+v_3}$

here, $v_1=6m/s$

$v_2=4m/s$

and $v_3=2m/s$

now, v = (2 × 6 × (4 + 2))/(2 × 6 + 4 + 2)

= 12 × 6/(12 + 6)

= 72/18

= 4 m/s

hence, average speed during the circular motion is 4m/s.