# Homework Help: A question about Rectilinear motion

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1. Apr 11, 2016

1. The problem statement, all variables and given/known data
Q:
If a particle moving along a straight line under uniform acceleration covers successive equal distances ( S each) in time intervals t1, t2 and t3 respectively, then the expression for average speed of particle in covering the given distance of 3S is:

Options:
A) (S/t1) + (S/t2) + (S/t3)
B) (S/t1) - (S/t2) + (S/t3)
C) 3S / (t1 + t2 + t3)
D) (S/t1) + (S/t2) - (S/t3)

[You may assume the particle is speeding up for the entire journey]

Here the correct answer are options B and C.
I cannot see how B is correct, although I easily got the option C.

2. Relevant equations
Average speed = Total distance covered / Total time taken

3. The attempt at a solution
Avg speed = (S + S + S) / (t1 + t2 +t3) = 3S / (t1+t2+t3)
This gives option C.
But I cannot get option B anyhow.

2. Apr 11, 2016

### Staff: Mentor

Good.

Hint: Each term in B is an average speed. Express those averages in terms of initial and final speed.

3. Apr 12, 2016

Okay then, I believe this is the way:
v2 will be average of v1 and v3
If the avg speeds are v1 = (S/t1) , v2 = (S/t2), v3 = (S/t3), then
Distance travelled during t2 is given by
S = v1t2 + 0.5at22 and also a = (v3 - v1)/t2 [using Newton's laws of motion]
∴ S = v1t2 + 0.5(v3 - v1)t2
⇒ (S/t2) = v1 + 0.5v3 - 0.5v1
⇒ 2(S/t2) = v1 + v3
⇒ 2(S/t2) = (S/t1) + (S/t3)
⇒ (S/t2) = (S/t1) - (S/t2) + (S/t3) = v2
⇒ vavg = v2 = (S/t1) - (S/t2) + (S/t3)

Am I correct?

4. Apr 13, 2016

### Staff: Mentor

Here's how I would look at it. For interval t1, let the initial and final speeds be v1 and v2. Express the average speed (S/t1) in terms of v1 and v2. Do the same for the other intervals and the total.

5. Apr 16, 2016