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Applying Relative Motion to One Dimensional Motion Equations

  1. Jul 9, 2015 #1
    <<Moderator note: LaTeX corrected>>

    Problem:
    > Two cars A and B move with velocity ##60 kmh^{-1}## and ##70 kmh^{-1}##. After a certain time, the two cars are 2.5 km apart. At that time, car B starts decelerating at the rate 20 kmh-2. How long does Car A take to catch up with Car B?

    I tried to apply Relative Motion Concept to try and solve this problem. However, I cannot understand how to apply it to this problem.

    My attempt:
    I tried to apply the Relative Motion Concept to this problem as follows.

    $$u_{AB}=u_A-u_B=60-70=-10kmh^{-1}$$
    As per the question, the separation between the two cars ie ##S_{AB}=-2.5km## after 15 minutes.

    Now, since Car A catches up with Car B eventually, thus ##S_{AB_{final}}=0## and ##S_{AB_{initial}}=-2.5km ##
    $$\Longrightarrow S_{AB_{final}}-S_{AB_{initial}}=0-(-2.5)=u_{AB}\times t + \dfrac{1}{2}a_{AB}\times t^2$$
    Now ##a_{AB}=a_A-a_B=0-(-20)=20kmh^{-2}## and ##u_{AB}=10kmh^{-1}##
    $$\Longrightarrow 2.5=10t+10t^2$$
    However, on solving this quadratic, I get a value of time which is incorrect. Would somebody please be so kind as to show me how to correctly apply the concept of Relative Motion here? I would be truly grateful for any assistance. Many thanks in advance!
     
    Last edited by a moderator: Jul 9, 2015
  2. jcsd
  3. Jul 9, 2015 #2

    Orodruin

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    You have used the wrong value for the velocity, you found earlier that ##u_{AB} = -10## km/h.
     
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