anonymous
  • anonymous
A particle moves along the x axis with velocity of v(t) m/s. Find the displacement and distance travelled over the given time interval for: a) v(t) = 3t-2 for 0 ≤ t ≤ 2 b) v(t) = |1-2t| for 0 ≤ t ≤ 2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
velocity is the derivative of distance so distance is the integral of velocity integral of (3t-2) = (3/2) t^2 - 2t d(t)=(3/2)t^2 -2t t=0 -> d(0)=0 t=1 -> d(1)=3/2 -2 = -1/2 t=2 -> d(2)=(3/2)(4) - 2(2) = 6-4 = 2
anonymous
  • anonymous
so displacement is 2 m and distanc is 8/3 m.
anonymous
  • anonymous
yes the displacement is 2, but i think the distance isn't 8/3. from t=0 to t=1 , the distance is 1/2 from t=1 to t=2, the distance is 2-(-1/2) = 3 so the total distance from t=0 to t=2 is 3 + 1/2 = 7/2

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anonymous
  • anonymous
at t=3/2 v=0 the particle changes its direction of motion , u need to consider that also while finding the distance hint:try plotting it on the x axis

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