Question

A particle moves in straight line with velocity 6 m/s and
3 m/s for time intervals which are in ratio 1:2. Find
average velocity.
(a) 2 m/s (6) 3 m/s (c) 4 m/s
(d) 5 m/s​

Answer 1

Answer:

Key Idea average velocity and instantaneous velocities have same value in a uniform motion. Average velocity is that uniform velocity with which the object will cover the same displacement in same interval of time as it does with actual variable velocity during that time interval.  

=(3m/s×20s)+(4m/s×20s)+(5m/s×20s)

=(60+80+100)−240m

Total time taken =20+20+20

                           =60s

∴ Average velocity =  

60

240

​  

=4m/s

Explanation:

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Answer 2

given,

V1 =  6m/s

V2 = 3 m/s

Time interval is in the ratio of  1: 2

then we can assume that,

t1 =  T

t2 = 2T

 So, total displacement of the particle is given by

D = V1 × t1 + V2 × t2

D   = 6× T +  3× 2T

 D =  6T + 6T

   D = 12 T

and, total time of motion is ,

T = T + 2T  = 3T

so, average velocity is

V avg  =  D/ T

    = 12T/ 3t

V avg =  4 m/s

Answer is 4 m/s.

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