What is the relationship between EMF and acceleration in a car?

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In summary, the EMF (Effective Motive Force) for a car is the engine driving force minus friction and air resistance. Using the impulse-momentum theorem, the net force applied to the car can be calculated to be 833 N, and the final speed reached is approximately 25 m/s. When the EMF is gradually increased by the driver during the 30 seconds, the net force becomes a linear function of time, resulting in a final speed of 250 m/s. However, when the driver increases the EMF gradually, the speed of the car remains constant over the first 30 seconds.
  • #1
Natasha1
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Cannot get the value for c??

The EMF (Effective Motive Force) for a car is the engine driving force minus friction and air resistance.

a)A car of mass 1000Kg travels from rest with constant acceleration to 25 m/s in 30 seconds. Use the impulse-momentum relationship to find the EMF?

b)Now suppose that instead the EMF is made by the driver to increase uniformly during the 30 seconds (by gradually increasing foot pressure on the accelerator). Use the impulse-momentum relationship to find the final speed reached?

c)Compare a) and b)?

Here is the working

The impulse-momentum theorem is:

[tex]
\overline{\sum F} \Delta t = \Delta p
[/tex]

where [tex]
\overline{\sum F}
[/tex] is the average net force applied to the object.

a) The acceleration is constant, so the net force applied is constant. I will call the net force F.


[tex]
F \Delta t = \Delta p = m \Delta v
[/tex]

[tex]
F = m \frac{ \Delta v}{ \Delta t} = 1000 \frac{25}{30} \, N
[/tex]

Thus F = 833 N.

b) The acceleration is now a linear function of time over the first 30 seconds of motion. Thus the net force is also a linear function of time. Using the Calculus version of the impulse-momentum theorem:
[tex]
\int_{t_0}^t F \,dt = \int_{v_0}^v m \, dv
[/tex]

The problem I am having here is that the acceleration is a linear function of time, and we don't have the constant: [tex]
a(t) = ct
[/tex] , giving [tex]
F(t)=ma(t)=mct
[/tex]

Is there anywhere I have gone wrong?

In terms of c:

[tex]
\int_0^{30}mct \, dt = \int_0^v m \, dv
[/tex]

[tex]
\frac{1}{2}mct^2|_0^{30} = mv|_0^v
[/tex]

[tex]
450mc=mv
[/tex]

[tex]
v = 450c \, \, m/s
[/tex]
 
Last edited:
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  • #2
Damn! I cannot make that \(\displaystyle writing work :-(\)
 
  • #3
type "tex" in place of "math".
 
  • #4
Natasha1 said:
Damn! I cannot make that \(\displaystyle writing work :-(\)
\(\displaystyle

Replace your math tags with [ tex ] tags, without the spaces. I'm just reading your question now.:smile:

~H\)
 
  • #5
On mathhelpforum.com you use the \(\displaystyle tag, but here use the [ tex ] tags. :)\)
 
  • #6
Jameson said:
On mathhelpforum.com you use the \(\displaystyle tag, but here use the [ tex ] tags. :)\)
\(\displaystyle

forgot a vital part of the question

b)Now suppose that instead the EMF is made by the driver to increase uniformly during the 30 seconds (by gradually increasing foot pressure on the accelerator), from 0 to a maximum which is twice the constant value in (a)). Use the impulse-momentum relationship to find the final speed reached?

Could anyone help please :-)\)
 
Last edited:
  • #7
Natasha1 said:
forgot a vital part of the question

b)Now suppose that instead the EMF is made by the driver to increase uniformly during the 30 seconds (by gradually increasing foot pressure on the accelerator), from 0 to a maximum which is twice the constant value in (a)). Use the impulse-momentum relationship to find the final speed reached?

Could anyone help please :-)

You should now be able 2 determine your constant. When t = 30, F = 2 x 833.

~H
 
  • #8
Hootenanny said:
You should now be able 2 determine your constant. When t = 30, F = 2 x 833.

~H


[tex]450m*0.0555333333=mv[/tex]

v = 250 ms-1 is this correct?
 
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  • #9
Wait a minute! There is no need for calculus here! What is the impluse - momentum relationship?

~H
 
  • #10
For par c)Compare a) and b)?

I answered that by gradually increasing foot pressure on the accelerator, the driver has increased by 10 folds the speed of the car. Is there anything else I should add?
 
  • #11
Natasha1 said:
[tex]450m*0.0555333333=mv[/tex]

v = 250 ms-1 is this correct?

I think you've made an error here. Sorry about my previous post, I was look at another topic.

~H
 
  • #12
Hootenanny said:
I think you've made an error here. Sorry about my previous post, I was look at another topic.

~H

I can't see any error, the m cancel out and v is = to what it's = to no?
 
  • #13
450 x 0.05553333333 [itex]\approx[/itex] 25

~H
 
  • #14
Hootenanny said:
450 x 0.05553333333 [itex]\approx[/itex] 25

~H

I did say that my calculator was playing up :redface:
 
  • #15
For par question c) Compare a) and b)?

I answered that by gradually increasing foot pressure on the accelerator, the driver does not change the speed of the car (over the first 30sec). Is there anything else I should add?
 
  • #16
Natasha1 said:
For par question c) Compare a) and b)?

I answered that by gradually increasing foot pressure on the accelerator, the driver does not change the speed of the car (over the first 30sec). Is there anything else I should add?

I would imagine that would be fine, unless they ask you to explain the fact you answer is good :smile:

~H
 
  • #17
Hootenanny said:
I would imagine that would be fine, unless they ask you to explain the fact you answer is good :smile:

~H

Thanks :-)
 

FAQ: What is the relationship between EMF and acceleration in a car?

What does the error message "Cannot get the value for c" mean?

This error message means that the program is unable to retrieve or assign a value to the variable c. This could be due to various reasons such as the variable not being declared or initialized properly, or there being an error in the code that prevents the value from being assigned.

How can I fix the "Cannot get the value for c" error?

To fix this error, you will need to check your code and ensure that the variable c is properly declared and initialized. Also, make sure that there are no errors in the code that could be preventing the value from being assigned. Debugging tools and techniques can also be used to identify the cause of the error.

Why am I getting the "Cannot get the value for c" error?

There could be several reasons why you are getting this error. Some common causes include typos in the variable name, forgetting to declare or initialize the variable, or an error in the code that prevents the value from being assigned. It is important to carefully review your code to identify the specific cause of the error.

Can a "Cannot get the value for c" error be caused by a logic error?

Yes, a logic error in the code can cause this error message. A logic error is when the code runs without producing any errors, but the output is incorrect. This can happen if there is an error in the logic or flow of the code that prevents the value from being assigned to the variable c.

How can I prevent the "Cannot get the value for c" error from occurring?

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