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A question about Rectilinear motion

  1. Apr 11, 2016 #1
    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. jcsd
  3. Apr 11, 2016 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Good.

    Hint: Each term in B is an average speed. Express those averages in terms of initial and final speed.
     
  4. Apr 12, 2016 #3
    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?
     
  5. Apr 13, 2016 #4

    Doc Al

    User Avatar

    Staff: Mentor

    I'm not sure I follow your reasoning.

    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.
     
  6. Apr 16, 2016 #5
    Thank you for helping me.
    The problem is solved.
     
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