What is the particle's distance from the origin

  • Thread starter TonkaQD4
  • Start date
  • Tags
    Origin
In summary, the position of a particle as a function of time is given by r = (6.50 ihat + 3.10 jhat)t^2 where t is in seconds. At t = 2.6 seconds, the particle is 0 meters away and has a speed of 0 m/. At t = 6.2 seconds, the particle is 276.8 meters away and has a speed of 19.2 m/.
  • #1
TonkaQD4
56
0
The position of a particle as a function of time is given by r = (6.50 ihat + 3.10 jhat)t^2 , where t is in seconds.

What is the particle's distance from the origin at t_1 = 2.6 seconds?
What is the particle's distance from the origin at t_2 = 6.2 seconds?

What is the particle's speed at t = 2.6 seconds?
What is the particle's speed at t = 6.2 seconds?

I know that at t = 0 seconds the particle is 0 meters away and has a speed of 0 m/.

How do I go about solving for the other questions?
 
Physics news on Phys.org
  • #2
Well I figured out that the magnitude of the vector r = (6.5+3.1)t^2 meters is 7.20.

Therefore I solved t = 2.6s... 7.2 x 2.6^2 = 48.7 meters and t = 6.2 s... 7.2 x 6.2^2 = 276.8 meters.

But now I am not sure of how to solve for the particle's speed?

Any help would be great.

Thanks
 
  • #3
TonkaQD4 said:
Well I figured out that the magnitude of the vector r = (6.5+3.1)t^2 meters is 7.20t^2.
You forgot to write a [itex]t^2[/itex] after the number, but I think you did it correct as you get the correct answer.

In one dimension, if the position of the particle is given by x(t), the velocity is given by x'(t). The same is true for (in this case) two dimensions: the derivative of the vector r(t) will give you the velocity vector v(t) = r'(t).
 
  • #4
So r'(t) = v(t)

I am not getting the right answer so maybe I am doing something wrong when taking the derivative..

r'(t) = 2(6.5+3.1)t or 19.2t Correct?
 
  • #5
No, the derivative is again a vector. It's not a number. If [itex]r(t) = (x(t), y(t), z(t)[/itex] in three dimensions, where x, y and z are just functions of t (the components of the vector), then [itex]r'(t) = (x'(t), y'(t), z'(t))[/itex] - the components are the derivatives of the original vector.
In this case [itex]r(t) = \left( 6.50 t^2 \hat \i + 3.10 t^2 \hat \j \right)[/itex]. The derivative is then
[tex]r'(t) = \left( \frac{d}{dt} 6.50 t^2 \hat \i + \frac{d}{dt} 3.10 t^2 \hat \j \right)
= \left( 2 \times 6.50 t \hat \i + 2 \times 3.10 t \hat \j \right),
[/tex]
which you can write as
[tex]r'(t) = (6.50 \hat \i + 3.10 \hat \j) 2 t[/tex].

I made the attached (very ugly!) image to show what I mean. The v(t) vector is supposed to be tangent to the black path of the object.
 

Attachments

  • path.jpg
    path.jpg
    10.8 KB · Views: 2,279
Last edited:
  • #6
TonkaQD4, did you get the correct answer using that^ equation? If so what is it because I can't seem to get it.
 
  • #7
Hi Becca.

Can you
a) not revive an old thread (the last post was almost 4 years ago)?
b) show some of your work? The answer is quite straightforward, so if you don't get it, it's most likely an algebraic error somewhere.
 
1.

What is the significance of a particle's distance from the origin?

The distance from the origin is a measure of how far the particle is from its starting point. It is an important factor in understanding the motion and behavior of particles in a system.

2.

How is the distance from the origin calculated?

The distance from the origin can be calculated using the Pythagorean theorem, which states that the distance between two points is equal to the square root of the sum of the squares of the differences in their coordinates. In other words, it is the length of the hypotenuse of a right triangle formed by the particle's coordinates.

3.

What units are used to measure the distance from the origin?

The distance from the origin is typically measured in units of length, such as meters or centimeters. The specific unit used may depend on the scale of the system being studied.

4.

Does the distance from the origin affect the particle's speed?

Yes, the distance from the origin can affect the particle's speed. The farther the particle is from the origin, the longer the distance it needs to travel to reach a specific point, which can result in a higher speed.

5.

How does the distance from the origin change over time?

The distance from the origin can change over time as the particle moves. It can increase, decrease, or remain constant depending on the direction and speed of the particle's motion. This change in distance can be represented by a displacement vector, which shows the change in position of the particle over time.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
827
  • Introductory Physics Homework Help
Replies
11
Views
910
  • Introductory Physics Homework Help
Replies
9
Views
750
  • Introductory Physics Homework Help
Replies
15
Views
253
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
485
  • Introductory Physics Homework Help
Replies
5
Views
975
  • Introductory Physics Homework Help
Replies
1
Views
676
  • Introductory Physics Homework Help
Replies
10
Views
487
  • Introductory Physics Homework Help
Replies
2
Views
734
Back
Top