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Physics Kinematics Application Question - Physics 11u

Wild ownz al

Member
Nov 11, 2018
30
In a 100 meter race, Maggie and Judy cross the finish line in a dead heat, both taking 10.2 seconds. Accelerating uniformly Maggie took 2.00 seconds and Judy 3.00 seconds to attain maximum speed, which they maintained for the rest of the race.

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?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
705
In a 100 meter race, Maggie and Judy cross the finish line in a dead heat, both taking 10.2 seconds. Accelerating uniformly Maggie took 2.00 seconds and Judy 3.00 seconds to attain maximum speed, which they maintained for the rest of the race.

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?
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?
 

Wild ownz al

Member
Nov 11, 2018
30
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?
These equations look great but how am I suppose to solve for the acceleration and V-final with two unknown variables in the formulas?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
705
These equations look great but how am I suppose to solve for the acceleration and V-final with two unknown variables in the formulas?
substitute $2a_m$ for $v_{fm}$ in the first equation

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


each equation will then have a single unknown
 

Wild ownz al

Member
Nov 11, 2018
30
Ok 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+(3aj)(7.2)

aj=3.83m/s^2
Vfj=12.00m/s

Is this correct?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
705
Ok 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?
$v_f$ for maggie is ok ... recheck your calculation for $v_f$ for judy
 

Wild ownz al

Member
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
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
705