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#### Wild ownz al

##### Member

- Nov 11, 2018

- 30

a)What was the acceleration of each sprinter?

b)What were their respective maximum speeds?

c)Which sprinter was ahead at the 6.00-second mark, and by how much?

- Thread starter Wild ownz al
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- Thread starter
- #1

- Nov 11, 2018

- 30

a)What was the acceleration of each sprinter?

b)What were their respective maximum speeds?

c)Which sprinter was ahead at the 6.00-second mark, and by how much?

- Mar 1, 2012

- 702

assuming both started from rest, base equation for motion of each runner ...

a)What was the acceleration of each sprinter?

b)What were their respective maximum speeds?

c)Which sprinter was ahead at the 6.00-second mark, and by how much?

total displacement = acceleration displacement + constant speed displacement

---------------------------------------------------------------------------------------

$100 = \dfrac{1}{2}a_m \cdot 2^2 + v_{fm} \cdot 8.2$ where $v_{fm} = a_m \cdot 2$

$100 = \dfrac{1}{2}a_j \cdot 3^2 + v_{fj} \cdot 7.2$ where $v_{fj} = a_j \cdot 3$

these equations should get you both accelerations and their respective final speeds ... can you take it from here?

- Thread starter
- #3

- Nov 11, 2018

- 30

These equations look great but how am I suppose to solve for the acceleration and V-final with two unknown variables in the formulas?assuming both started from rest, base equation for motion of each runner ...

total displacement = acceleration displacement + constant speed displacement

---------------------------------------------------------------------------------------

$100 = \dfrac{1}{2}a_m \cdot 2^2 + v_{fm} \cdot 8.2$ where $v_{fm} = a_m \cdot 2$

$100 = \dfrac{1}{2}a_j \cdot 3^2 + v_{fj} \cdot 7.2$ where $v_{fj} = a_j \cdot 3$

these equations should get you both accelerations and their respective final speeds ... can you take it from here?

- Mar 1, 2012

- 702

substitute $2a_m$ for $v_{fm}$ in the first equationThese equations look great but how am I suppose to solve for the acceleration and V-final with two unknown variables in the formulas?

substitute $3a_j$ for $v_{fj}$ in the second equation

each equation will then have a single unknown

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- #5

- Nov 11, 2018

- 30

For maggie:

100=1/2am(2^2)+(2am)(8.2)

am=5.43m/s^2

Vfm=10.87m/s

For Judy:

100=1/2aj+(3aj)(7.2)

aj=3.83m/s^2

Vfj=12.00m/s

Is this correct?

- Mar 1, 2012

- 702

$v_f$ for maggie is ok ... recheck your calculation for $v_f$ for judyOk using that logic I got the following:

For maggie:

100=1/2am(2^2)+(2am)(8.2)

am=5.43m/s^2

Vfm=10.87m/s

For Judy:

100=1/2aj(3^2)+(3aj)(7.2)

aj=3.83m/s^2

Vfj= 3aj ...

Is this correct?

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- #7

- Nov 11, 2018

- 30

Judy's Vf is 11.49m/s?

aj = 3.83m/s^2

Vfj = 3aj

Vfj=3(3.83m/s^2)

Vfj=11.49m/s

aj = 3.83m/s^2

Vfj = 3aj

Vfj=3(3.83m/s^2)

Vfj=11.49m/s

- Mar 1, 2012

- 702

yepJudy's Vf is 11.49m/s?

aj = 3.83m/s^2

Vfj = 3aj

Vfj=3(3.83m/s^2)

Vfj=11.49m/s