# PhysicsKinematics Application Question - Physics 11u

#### Wild ownz al

##### Member
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
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
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
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
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
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
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
Judy's Vf is 11.49m/s?

aj = 3.83m/s^2

Vfj = 3aj
Vfj=3(3.83m/s^2)
Vfj=11.49m/s
yep