Question

A particle moves along x axis with speed 6m/s for the firdt half distance of a journey and the second half with a speed 3m/s. What is The average speed in the total journey?

Answer 1

Your answer is --

Let , the total distance be 2d

Now ,

▪️In first case

Speed of particle S1 = 6m/s
Distance d1 = d

So, time t1 = d/S1 = (d/6)sec


▪️In second case

speed of particle S2 = 3m/s
distance d2 = d

So, time t2 = d/S2 = (d/3)sec


Now,

total time T = t1 + t2 = d/6 + d/3 = (3d/6)sec

Therefore ,

average speed = total distance/total time

= 2d/(3d/6)

= 4m/s


Henec, average speed is 4m/s

Answer 2

s=d/t

so,d=A meter ,s1=6m/s ,t1=d/t1 i.e; t1=A/6

d=A m ,s2=3m/s ,t2=d/s2 i.e; t2=A/3

average speed=(d+d)/(t1+t2)

=2A/(A/6+A/3)

=2A/(A/6+2A/6)

=2Ax6/(A+2A)

=12A/3A

=4m/s