If a rock is thrown upward o the planet Mars with a velocity of 10m/s, its height in meters t seconds later is given by y = 10 t − 1.86 t 2 a) Find the average velocity over the given time intervals:i)[1,2] ii)[1,1.5] iii)[1,1.1] iv)[1,1.01] v) [1,1.001]b) Estimate the instantaneous velocity when t=1.

Question

If a rock is thrown upward o the planet Mars with a velocity of 10m/s, its height in meters t seconds later is given by   y  =  10  t  −  1.86      t          2      a) Find the average velocity over the given time intervals:i)[1,2] ii)[1,1.5] iii)[1,1.1] iv)[1,1.01] v) [1,1.001]b) Estimate the instantaneous velocity when t=1.

Lukas Bryan · Accepted Answer

a)i) For the interval [1,2], the rock goes from a heightof   y  (  1  )  =  10  ∗  1  −  1.86  ∗  (  1      )    2    =  8.14  m. to a height of   y  (  2  )  =  10  ∗  2  −  1.86  (  2      )    2    =  12.56  m. so the average velocity is  △  s      /    △  t  =  (  12.56  −  8.14  )      /    (  2  −  1  )  =  4.42  m      /    sSimilarly,ii) For the interval   [  1  ,  1.5  ]  ,  y  (  1.5  )  =  10  ∗  1.5  −  1.86  (  1.5      )    2    =  10.815  m so the average vel.is  △  s      /    △  t  =  (  10.815  −  8.14  )      /    (  1.5  −  1  )  =  5.35  m      /    siii)For the interval   [  1  ,  1.1  ]  ,  y  (  1.1  )  =  10  ∗  1.1  −  1.86  (  1.1      )    2    =  8.7494  m so the average vel.is  △  s      /    △  t  =  (  8.7494  −  8.14  )      /    (  1.1  −  1  )  =  6.094  m      /    siv)For the interval   [  1  ,  1.01  ]  ,  y  (  1.01  )  =  10  ∗  1.01  −  1.86  (  1.01      )    2    =  8.20  m so the average vel.is  △  s      /    △  t  =  (  8.20  −  8.14  )      /    (  1.01  −  1  )  =  6  m      /    siv)For the interval   [  1  ,  1.001  ]  ,  y  (  1.001  )  =  10  ∗  1.001  −  1.86  (  1.001      )    2    =  8.15  m so the average vel. is  △  s      /    △  t  =  (  8.15  −  8.14  )      /    (  1.001  −  1  )  =  10  m      /    sb)for the instantaneous velocity at t=1  d  y      /    d  t  =  10  −  3.72  t  =  10  −  3.72  ∗  1  =  10  −  3.72  =  6.28  m      /    s

If a rock is thrown upward o the planet Mars with a velocity of 10m/s, its height in meters t seconds later is given by y=10t-1.86t^2 a) Find the average velocity over the given time intervals: i)[1,2] ii)[1,1.5] iii)[1,1.1] iv)[1,1.01] v) [1,1.001] b) Estimate the instantaneous velocity when t=1.

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