# Solving Curvilinear Motion: Find Velocity at t=3s

• MHB
• NotaMathPerson
In summary: Hi, Sr, I would like to know if you finally resolve...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.
NotaMathPerson
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.

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:
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.

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.

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?

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.

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:

in the minute 6:37

I really appreciate.

## What is curvilinear motion?

Curvilinear motion refers to the motion of an object along a curved path, rather than a straight line. This type of motion is common in nature and can be seen in various phenomena such as the motion of planets around the sun or the trajectory of a thrown ball.

## What is the equation for finding velocity at a given time?

The equation for finding velocity at a given time in curvilinear motion is v(t) = ds/dt, where v(t) represents the velocity at time t, s represents the position of the object along the curved path, and t represents time. This equation is based on the fundamental principle of calculus, where velocity is the derivative of position with respect to time.

## How do you solve for velocity in curvilinear motion?

To solve for velocity in curvilinear motion, you need to know the position function of the object and use the derivative of this function with respect to time. This derivative will give you the velocity at any given time. You can also use the arc length formula, which involves finding the rate of change of distance over time, to calculate velocity in curvilinear motion.

## What does velocity at t=3s represent?

Velocity at t=3s represents the speed and direction of the object at a specific point in time, in this case, at 3 seconds. It is a measure of how fast the object is moving along the curved path at that particular moment.

## What are some real-life applications of solving curvilinear motion?

Curvilinear motion is used in various fields such as physics, engineering, and astronomy. It is essential in understanding and predicting the motion of celestial bodies, designing roller coasters and other amusement park rides, and studying the movement of fluids. It is also used in sports, such as calculating the trajectory of a ball in sports like baseball and football.

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