# Kinematics Application Question - Physics 11u

• MHB
• Wild ownz al
In summary: So in summary, both sprinters have different accelerations and maximum speeds, but they both cross the finish line in a dead heat with a time of 10.2 seconds. At the 6.00-second mark, Maggie was ahead by 2.74 meters.
Wild ownz al
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?

Wild ownz al said:
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?

skeeter said:
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?

Wild ownz al said:
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 equationeach equation will then have a single unknown

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?

Wild ownz al said:
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

Judy's Vf is 11.49m/s?

aj = 3.83m/s^2

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

Wild ownz al said:
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

## 1. What is Kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the causes of the motion (e.g. forces). It involves analyzing the position, velocity, and acceleration of objects as they move through space and time.

## 2. What is a Kinematics Application Question?

A Kinematics Application Question is a problem that requires the application of kinematics principles and equations to solve. These types of questions often involve real-world scenarios and require the use of formulas such as distance, velocity, and acceleration to find the desired solution.

## 3. How do I approach a Kinematics Application Question?

The first step in approaching a Kinematics Application Question is to carefully read and understand the given information and identify what is being asked. Then, use the appropriate kinematics equations and plug in the given values to solve for the unknown variable. It is important to pay attention to units and use the correct formula for the given scenario.

## 4. What are some common formulas used in Kinematics?

Some common formulas used in Kinematics include:

- s = ut + 1/2at^2 (equation for displacement)

- v = u + at (equation for final velocity)

- v^2 = u^2 + 2as (equation for final velocity squared)

- a = (v-u)/t (equation for acceleration)

## 5. How can Kinematics be applied in real-life situations?

Kinematics can be applied in various real-life situations, such as calculating the speed and distance of a moving car, predicting the trajectory of a projectile, or determining the time it takes for an object to fall from a certain height. It can also be used in sports, such as calculating the trajectory of a soccer ball or the acceleration of a sprinter. Understanding kinematics can help us analyze and predict the motion of objects in our daily lives.

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