# A Point traversed half the distance with a velocity V1. The remaining part of the distance was covered with velocity V2 for half the time and with velocity V3 for the other half time. Find the mean velocity of the point aveaged over the whole time of motion.

Swapnil Saxena
102 Points
11 years ago

Hi Vivek,

Let the total distance be D.

Let the point transversed half the distance by velocity V1.

Then the time required by it to do so = (D/2)/V1 = D/2V1

The remaining half was transversed by travelling at V2 for halftime and V3 velocity for another half time.

Let the time to cover the second half of the journey = t

Then V2t/2+V3t/2= D/2(Second Half of journey)

So t= D/(V2+V3)

The total time required for the journey is (D/2V1)+(D/(V2+V3))

The Average or mean Velocity = D/( (D/2V1) + (D/(V2+V3)) ) = 1/( (1/2V1) + (1/(V2+V3)) ) =2V1(V2+V3)/(2V1+V2+V3)----------(ans)

sannisth soni
5 Points
11 years ago
Hello Vivek,

see, if u wanna find average velocity of two different velocities if time is same then apply 2*V1V2/V1+V2... nd if distances travelled by two different velocities is d same then apply V1+V2/2.
In this question,in the second half of distance, the time period is the same. So, the avg. velocity will be 2*V2V3/V2+V3. In, the first part of the quetion the avg. velocity is V1 as its maintained all d way.
Now the velocities 2*V3V2/V3+V2 and V1 are the velocities by which the distances travelled are the same. So, the avg. velocity will be {2*V2V3/V2V3} + {V1}/2=2V1{V2+V3}/2V1+V2+V3
Hope the answer is correct nd it helped.....all d best
Vivek Raj
15 Points
11 years ago
Thanks for your kind help>>>>>>>
User
13 Points
4 years ago
Ok let`s start Let S1 is the first j
Saanvi
15 Points
4 years ago
V1(V2+V3)+2V1V2/2(V1+V2) . This is my answer.........................................................................................
askIITians Faculty 628 Points
2 years ago
Let us assume that the total length of journey = d
Now, The time taken by the point to cover the first half of the distance, t1 = d/(2 x V1)
Let the time taken to cover second half of distance = t2
The remaining distance is covered with velocities of V2 and V3 in equal time intervals = t2/2
Now since total distance covered in second half of journey = d/2 = V2 x t2/2 + V3 x t2/2
on simplifying, we get,
t2 = d/(V2 + V3)

Hence, total time of journey = t1 + t2 = d/2V1 + d/(V2 + V3)

Hence, average speed of journey = total distance covered during journey/ time taken in the journey
= d / [  { d/2V1 } + { d/(V2 + V3) }  ] = 1 / [ { 1/2V1 } + { 1/(V2 + V3) } ]
= 2V1(V2 + V3(2V1 + V2 + V3)