Advanced One Dimensional Kinematic Problem

In summary, a car traveling at 25 m/s collides with a utility pole, causing the driver to continue moving at the same speed. The airbag, starting from rest 50 cm away from the driver, makes contact in 9 ms. To find the acceleration of the airbag, the distance traveled by the driver must first be calculated by subtracting it from the initial distance of 50 cm. This value is then plugged into the equation for displacement, along with the time and initial velocity of 0 m/s, to solve for the acceleration of the airbag.
  • #1
LexRunner
7
0
A car is traveling at 25 m/s when it runs off the road and hits a utility pole. The car stops instantly, but the driver continues to move forward at 25 m/s. The airbag starts from rest with a constant acceleration from a distance of 50 cm away from the driver and makes contact with him in 9 ms. What is the acceleration of the airbag?

My answer was a = 1234.568 m/s, but its wrong.

These were what I believe to have been the known quantities:
vi = 0
a = ?
t = 0.009 s
d = 0.050 m

I used this equation to solve the problem:
d = vit + 1/2*a*t2

What am I doing wrong and what is the right answer?
Thanks
 
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  • #2
How many meters is 50 cm equivalent to?
 
  • #3
LexRunner said:
A car is traveling at 25 m/s when it runs off the road and hits a utility pole. The car stops instantly, but the driver continues to move forward at 25 m/s. The airbag starts from rest with a constant acceleration from a distance of 50 cm away from the driver and makes contact with him in 9 ms. What is the acceleration of the airbag?

My answer was a = 1234.568 m/s, but its wrong.

These were what I believe to have been the known quantities:
vi = 0
a = ?
t = 0.009 s
d = 0.050 m

I used this equation to solve the problem:
d = vit + 1/2*a*t2

What am I doing wrong and what is the right answer?
Thanks
The driver was moving, so the airbag does not have to travel the full 50 cm. The bag and the driver must travel that distance so the airbag will travel a smaller distance.

By the way, the answer will be in ##m/s^2##, not ##m/s##.
 
  • #4
nrqed said:
The driver was moving, so the airbag does not have to travel the full 50 cm. The bag and the driver must travel that distance so the airbag will travel a smaller distance.

By the way, the answer will be in ##m/s^2##, not ##m/s##.


So you're saying my other quantities are correct, except the quantity for distance because the driver will still be moving forward while the airbag is coming out so he distance would be less than 50 cm. So if I found the right distance, and plugged it into the equation, I would gt the right answer?
 
  • #5
So to find the distance the airbag traveled, I would have to take 50 cm subtracted by the distance the man traveled. These would by my known quantities:
V(initial): 25 m/s
V(final): 0 m/s (because he hits the airbag)
T: 0.009 s (convert 9 ms to sec)
D: ?

So I would have to plug his into find the distance the man travelled, take 50 cm subtracted by the value of D to find the distancetthe airbag traveled and plug the result into the original equation to find the acceleration of the airbag.
 
  • #6
Apparently you are working in a reference frame attached to the car. Which is standing still against the utility pole when the airbag takes off.
So to find the distance the airbag traveled, I would have to take 50 cm subtracted by the distance the man traveled.
is indeed correct. Please calculate this distance, which under point 1. has been called d, and show.
Now the airbag.
The airbag starts from rest with a constant acceleration
so you apply the relevant equation (so conveniently listed under 2. relevant equations. In the template.)
d = vit + 1/2*a*t2
What is vi if it starts from rest ?

This gives you the so desired a. Note that vf is not zero. The man hits the bag with 25 m/s for the man and vf (which should be considerable) in the other direction for the bag. It's not a sandbag, it's an airbag.

Ceterum censeo that this kind of exercises is didactically irresponsible: there is nothing realistic about it, it's full of unsound physics, etc. etc.

Nevertheless: welcome to PF, Lex ! Not your fault what I fulminate against in the last paragraph!
 
  • #7
You know how far the man travelles (in metres) in 0.009 seconds, its : v * t = 25.0 * 0.009 = 0.225 m
Subtract that from 0.5 m to get the distance traveled by the airbag (s), then :
a = ( s - ( u * t ) ) / ( ½ * t ² )
( t = 0.009 s, u = 0.0 )
 
  • #8
Thanks, Dean. But the intention was that Lex should do and show the work...:smile:
 

Related to Advanced One Dimensional Kinematic Problem

1. What is an advanced one dimensional kinematic problem?

An advanced one dimensional kinematic problem is a type of physics problem that involves analyzing the motion of an object in a straight line, taking into account factors such as velocity, acceleration, and displacement. These types of problems often require the use of advanced mathematical equations and techniques.

2. How do I solve an advanced one dimensional kinematic problem?

To solve an advanced one dimensional kinematic problem, you will need to first identify the given variables and determine what is being asked in the problem. Then, you can use equations such as the kinematic equations or the equations of motion to solve for the unknown variable. It is important to carefully set up your equations and plug in the correct values to get an accurate answer.

3. What are some common strategies for solving advanced one dimensional kinematic problems?

Some common strategies for solving advanced one dimensional kinematic problems include drawing a diagram to visualize the problem, breaking down the problem into smaller parts, and using the correct equations for the given scenario. It is also helpful to double check your work and make sure your final answer makes sense in the context of the problem.

4. What are some real-world applications of advanced one dimensional kinematic problems?

Advanced one dimensional kinematic problems can be used to analyze the motion of objects in various real-world scenarios, such as calculating the speed of a car on a straight road or determining the displacement of a falling object. These types of problems are also important in fields such as engineering, where understanding the motion of objects is crucial in designing and building structures and machines.

5. What are the limitations of using advanced one dimensional kinematic equations?

One limitation of using advanced one dimensional kinematic equations is that they only apply to objects moving in a straight line with constant acceleration. In real-world scenarios, objects may experience non-constant acceleration or may move in more complex paths, making it difficult to accurately apply these equations. Additionally, these equations do not take into account other factors such as air resistance or friction, which can affect the motion of objects in the real world.

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