Solving Curvilinear Motion: Find Velocity at t=3s

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    Curvilinear Motion
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Discussion Overview

The discussion revolves around solving a problem related to curvilinear motion, specifically determining the velocity of an object at a given time based on its acceleration function, initial velocity, and position. Participants explore the integration of acceleration to find velocity components and address the role of initial conditions.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the acceleration function and initial conditions, attempting to integrate the acceleration to find velocity components.
  • Another participant notes the necessity of including integration constants after integrating the acceleration components.
  • There is a discussion about how to determine the integration constants using the initial velocity.
  • Participants debate the correct interpretation of the integration constants, with some suggesting they should all be zero due to the initial position being at the origin.
  • One participant expresses confusion about whether the sum of the constants is zero or if each constant is individually zero.
  • Another participant clarifies that the constants are separate and should not be summed.
  • There is a request for assistance in completing the problem, indicating uncertainty about the final steps needed to find the solution.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the treatment of integration constants, and there remains uncertainty about the final calculations and the approach to finding the position magnitude. The discussion reflects multiple competing views on how to proceed with the problem.

Contextual Notes

Participants express uncertainty regarding the integration process and the implications of initial conditions on the constants. There are unresolved questions about the calculations and the final answers related to both velocity and position.

NotaMathPerson
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The acceleration function of an object doing curvilinear motion is a = {(-0.2t)i+2j+1.5k} m/s^2, where t is in s. If its initial velocity v0 = 8i m/s, and initial position is at the origin, determine the magnitude of its velocity when t=3 s.

Badly need your help guys. Thanks!

All I see is

ax = -0.2t
ay = 4
az = 1.5

Integrating all components i have

Vx= t^2/10 m/s
Vy = 2t m/s
Vz = 1.5t m/s

@ t = 3s

I get V = 7.554 m/s

But I ignored V0 which i don't know the use of.
 
Last edited:
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Re: Curvelinear motion

NotaMathPerson said:
The acceleration function of an object doing curvilinear motion is a = {(-0.2t)i+2j+1.5k} m/s^2, where t is in s. If its initial velocity v0 = 8i m/s, and initial position is at the origin, determine the magnitude of its velocity when t=3 s.

Badly need your help guys. Thanks!

All I see is

ax = -0.2t
ay = 4
az = 1.5

Integrating all components i have

Vx= t^2/10 m/s
Vy = 2t m/s
Vz = 1.5t m/s

@ t = 3s

I get V = 7.554 m/s

But I ignored V0 which i don't know the use of.

Hi NotaMathPerson! :)

After integration, we should have an integration constant.
The velocity should be:
$$v_x= (t^2/10 + C_1) \text{ m/s} \\
v_y = (2t + C_2) \text{ m/s} \\
v_z = (1.5t + C_3)\text{ m/s} $$

We can substitute $t=0$ to find the initial velocity and set it equal to the given initial velocity.
 
Re: Curvelinear motion

I like Serena said:
Hi NotaMathPerson! :)

After integration, we should have an integration constant.
The velocity should be:
$$v_x= (t^2/10 + C_1) \text{ m/s} \\
v_y = (2t + C_2) \text{ m/s} \\
v_z = (1.5t + C_3)\text{ m/s} $$

We can substitute $t=0$ to find the initial velocity and set it equal to the given initial velocity.

How is that going lead me to the velocity @ t=3s?
 
Re: Curvelinear motion

NotaMathPerson said:
How is that going lead me to the velocity @ t=3s?

It allows you to find $C_1$, $C_2$, and $C_3$ (which is effectively just the initial velocity).
After that you can substitute $t=3$ and find the velocity at that time.
 
Re: Curvelinear motion

I like Serena said:
It allows you to find $C_1$, $C_2$, and $C_3$ (which is effectively just the initial velocity).
After that you can substitute $t=3$ and find the velocity at that time.

You said that i can substitute t =0 to the components equation

C1 = 8, C2 = 0 C3 = 0

(t^2/10+8)i +2tj+1.5k = V

@ t = 3s
89/10i+6j+4.5k = V

Vmag = 11.639 m/s is this correct?What if The problem also ask for the magnitude of the position what should I do?
 
Last edited:
Re: Curvelinear motion

NotaMathPerson said:
You said that i can substitute t =0 to the components equation

C1 = 8, C2 = 0 C3 = 0

(t^2/10+8)i +2tj+1.5k = V

@ t = 3s
89/10i+6j+4.5k = V

Vmag = 11.639 m/s is this correct?What if The problem also ask for the magnitude of the position what should I do?

It looks correct (without checking the calculations), although you left out a $t$ in the k-component of the formula for the velocity.

To find the position, integrate the equations you have for the velocity (including the missing $t$), and use the fact that the initial position is at the origin - it's the same thing!
 
Re: Curvelinear motion

I like Serena said:
It looks correct (without checking the calculations), although you left out a $t$ in the k-component of the formula for the velocity.

To find the position, integrate the equations you have for the velocity (including the missing $t$), and use the fact that the initial position is at the origin - it's the same thing!

Do I have to also put an integration constant after integrating?
 
Re: Curvelinear motion

NotaMathPerson said:
Do I have to also put an integration constant after integrating?

Yes.
In this particular case all three constants will turn out to be zero since it is given that the initial position is at the origin.
 
Re: Curvelinear motion

NotaMathPerson said:
Do I have to also put an integration constant after integrating?
Didn't you learn that in Calculus I? If F is an anti-derivative of f, that is, if F'= f, then so is F+ C for any constant C.
 
  • #10
Re: Curvelinear motion

I like Serena said:
Yes.
In this particular case all three constants will turn out to be zero since it is given that the initial position is at the origin.

Hello.

Do you mean the sum of the three constants is zero?

Because when I integrate and let t =0. I get Ca + Cb + Cc = 0 . What do you mean by all three constants are zero? Do you mean individually?
 
  • #11
No! We did not sat that and did not mean that! The three components of the vector are separate functions. They are not to be added.
 
  • #12
Re: Curvelinear motion

NotaMathPerson said:
Hello.

Do you mean the sum of the three constants is zero?

Because when I integrate and let t =0. I get Ca + Cb + Cc = 0 . What do you mean by all three constants are zero? Do you mean individually?
Hi, Sr, I would like to know if you finally resolve this problem, I really do not know how to finish...do you the solution?
I am interested in this problem becouse I saw it in this link:

https://www.youtube.com/watch?v=gQMijT0hZdk&index=6&list=PLLbvVfERDon1xk3wGaYfXSmGa1u83mGn-

in the minute 6:37

I really appreciate.
 

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