Kinetics Question: Solving for Velocity and Displacement

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In summary: If b=-1 then the train will travel in the negative direction and you will end up with a negative distance. Examine the given equation(velocity) and you will notice that "b" is the constant which makes the velocity to be positive or negative. If b=1 then the train will travel in the positive direction and you will end up with positive distance. If b=-1 then the train will travel in the negative direction and you will end up with a negative distance.
  • #1
uzman1243
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Homework Statement


attachment.php?attachmentid=72422&stc=1&d=1408927480.png


Homework Equations




The Attempt at a Solution


v = ds/dt

∫v dt = ∫ds

(put all inital values for V)
∫70-70e^t dt = ds

70t - 70t*e^t = s

There is something wrong with my methodology. can you guide me here?
 

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  • #2
Looks like you did not integrate [itex]e^{-bt}[/itex] correctly. Check you last eqution. You have something extra there.
 
  • #3
uzman1243 said:
∫70-70e^t dt = ds

70t - 70t*e^t = s

Are you sure that is the correct integral?


Edit:
Sorry, I didn't see Mr-R's post when I posted this
 
  • #4
Mr-R said:
Looks like you did not integrate [itex]e^{-bt}[/itex] correctly. Check you last eqution. You have something extra there.

∫v0 (1-e^(-b*t))

∫v0 - v0*e^(-b*t)

= v0*t - V0*e^(-b*t) + c

is that correct?
 
  • #5
uzman1243 said:
∫v0 (1-e^(-b*t))

∫v0 - v0*e^(-b*t)

= v0*t - V0*e^(-b*t) + c

is that correct?
Well the constant c is nice :smile:. Missing something from [itex]e^{-bt}[/itex] when you intagrated it though.

Edit: are you writing b explicitly or just its value? If you just substitute its value there then your integral is correct. (looks like you did not)
 
Last edited:
  • #6
Mr-R said:
Well the constant c is nice :smile:. Missing something from [itex]e^{-bt}[/itex] when you intagrated it though.

Edit: are you writing b explicitly or just its value? If you just substitute its value there then your integral is correct. (looks like you did not)

Can you show me the integration?
 
  • #7
uzman1243 said:
Can you show me the integration?

Of course I can, but I know you can do it by yourself so I will give an example.

[itex]∫e^{Cx}dx=\frac{1}{C}e^{Cx}+c[/itex]

Can you see you mistake and fix your integral now?
 
  • #8
Mr-R said:
Of course I can, but I know you can do it by yourself so I will give an example.

[itex]∫e^{Cx}dx=\frac{1}{C}e^{Cx}+c[/itex]

Can you see you mistake and fix your integral now?

v0*t + (V0*e^(-b*t))/b + c

Yes. That should be it? Now I sub in all the values and find the constant C and my final answer for distance is -1126m. The answer is correct but it should be a positive value.
Is this because my answer is displacement and the question requires distance (just magnitude only)?
 
  • #9
uzman1243 said:
v0*t + (V0*e^(-b*t))/b + c

Yes. That should be it? Now I sub in all the values and find the constant C and my final answer for distance is -1126m. The answer is correct but it should be a positive value.
Is this because my answer is displacement and the question requires distance (just magnitude only)?

Well the function describes a train moving with a velocity that has a negative sign(if b=-1 see below). If they defined the positive direction to be the right direction. Then the function gives you a backwards moving train.

See the attached file,

The first graph is your given equation (velocity). The second graph is the distance which you found by integrating.

Examine the given equation(velocity) and you will notice that "b" is the constant which makes the velocity to be positive or negative. If b=1 then the train will travel in the positive direction and you will end up with positive distance.
 

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What is the formula for velocity?

The formula for velocity is v = d/t, where v represents velocity, d represents displacement, and t represents time.

How do you solve for velocity?

To solve for velocity, you need to know the displacement and the time. Then, you can use the formula v = d/t to calculate the velocity.

What is displacement?

Displacement is the distance and direction an object moves from its original position. It is a vector quantity and is represented by the symbol d.

What units are used to measure velocity and displacement?

Velocity is typically measured in meters per second (m/s) or kilometers per hour (km/h), while displacement is measured in meters (m) or kilometers (km).

How is velocity related to acceleration?

Velocity and acceleration are related because acceleration is the rate of change of velocity over time. In other words, acceleration measures how quickly an object's velocity is changing. The formula for acceleration is a = (v2 - v1)/t, where a represents acceleration, v2 represents final velocity, v1 represents initial velocity, and t represents time.

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