Question

The displacement (in meters) of an object moving in a straight line is given by s=1+2t+1/4t^2^2, where t is measured in seconds. Find the avg velocity over each time period, a) [1,3]

Answer 1

 (A) 
  s{ t } = (¼)t² + 2t + 1  ...  differentiate to get velocity versus time 

  v{ t } = (½)t + 2  ...  linearly increases with time 

(1) 

 Vavɢ{  a→b  } = [ v{ b } + v{ a } ] ⁄ 2 
 Vavɢ{ 1→3  } = [ v{ 3 } + v{1 } ] ⁄ 2 
 Vavɢ{ 1→3  } = [ (½)(3) + 2 + (½)(1) + 2 ]  ⁄  2 
 Vavɢ{ 1→3  } = 3 m/sec 

(II) and (III) are done the same way. 

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(B) 
    v{ t } = (½)t + 2 

   v{1 } = (½)(1) + 2 
   v{1 } = 2.5 m/sec