A Maths questions on differentiation and integration

• amaths

  10 Feb 09, 00:54

  Hi, would be grateful if anyone out there can provide the proof to the following question: The speed v m/s of a particle travelling from A to B, at time t seconds after leaving A, is v=10t-t^2. The particle starts from rest at A and comes to rest at B. Prove that the particle has a speed of 5 m/s or greater for exactly 4*(5^0.5) seconds.
• amaths

  10 Feb 09, 01:00

  Hello, something seems to be wrong with the power sign (ie, ^), so here is the question again. Thanks and cheers. ====== Hi, would be grateful if anyone out there can provide the proof to the following question: The speed v m/s of a particle travelling from A to B, at time t seconds after leaving A, is v=10t-t^2. The particle starts from rest at A and comes to rest at B. Prove that the particle has a speed of 5 m/s or greater for exactly 4*(square root of 5) seconds.
• Mikethm

  10 Feb 09, 04:28

  When V=5

  10t-t^2=5

  t^2-10t+5=0

  using quadratic formula, u get...

  t = 5- 2[sqrt(5)] or t = 5 +2[sqrt(5)]

  The graph of V is n shaped. It hit V=5 at 5-2[sqrt(5)] and fall to V=5 at 5+2[sqrt(5)].

  Thus time interval for which speed = 5m/s or greater

  ={5+2[sqrt(5)]} -{5-2[sqrt(5)]}

  = 4sqrt5 ( proven)

   

• eagle

  10 Feb 09, 16:23

  Wah... Mike 4.38am still not yet sleep ah

• Mikethm

  10 Feb 09, 22:09

  Originally posted by eagle:

  Wah... Mike 4.38am still not yet sleep ah

  Don't you sleep in the morning like me? I thought all tutors are vampires no?

• eagle

  10 Feb 09, 22:38

  Originally posted by Mikethm:

  Don't you sleep in the morning like me? I thought all tutors are vampires no?

  lol

  I still got full time work... tuition after work only...