2d Motion, calculating time when v=0 from position vector

In summary, The position vector of a particle is given by r= ihat(2t^3-21t^2+60t+10) +jhat(3/2)(t^2-10t+9). The velocity vector can be found by taking the derivative of the position vector. To find the time at which the velocity is zero, both components of the velocity vector must be set to zero simultaneously.
  • #1
bearandmoose
1
0

Homework Statement


The position vector of a particle is given by r= ihat(2t^3-21t^2+60t+10) +jhat(3/2)(t^2-10t+9)
At what time, if any, is the velocity of the particle zero (ie what time is the particle instantaneously at rest)



Homework Equations





The Attempt at a Solution


Finding the velocity vector is simple, just taking the derivative of position
However, when I set that to 0 I have the ihat and the jhat and I don't know how to combine them to solve for the time. Is this even the right step?

If I take
v= (6t^2-42t+60)ihat+(3t^2-15)jhat
and set that to 0
how do I account for the vx and vy when setting that to 0?
Do I set vx and vy to 0 separately?

I'm really confused.

Thanks.
 
Physics news on Phys.org
  • #2
In order for v to be zero, both components must be zero. (at the same time, of course)
 

1. What is 2d motion and how is it different from 1d motion?

2d motion refers to the movement of an object in a two-dimensional space, while 1d motion refers to movement in a single dimension. In 2d motion, an object's position is described by two coordinates, typically x and y, while in 1d motion, only one coordinate is needed. This means that 2d motion involves both horizontal and vertical movement, while 1d motion only involves movement along a single axis.

2. How do you calculate time when velocity is equal to 0?

To calculate time when velocity is equal to 0, you can use the formula t = (xf - xi)/v, where t is the time, xf is the final position, xi is the initial position, and v is the velocity. This formula is derived from the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration (assumed to be 0 in this case), and t is the time. By rearranging the equation, we can solve for time when velocity is equal to 0.

3. Can you explain the concept of position vector in 2d motion?

In 2d motion, the position vector refers to a vector that represents the position of an object in a two-dimensional space. It is typically denoted as r and can be written as r = xi + yj, where xi represents the horizontal position and yj represents the vertical position. The magnitude of the position vector represents the distance of the object from the origin, while the direction of the vector represents the direction of the object's movement.

4. How is time related to displacement in 2d motion?

In 2d motion, time is directly related to displacement. The displacement of an object is the change in its position over a certain amount of time. This means that as time increases, the displacement of the object also increases. Additionally, the rate at which the object's displacement changes over time is equal to its velocity.

5. Can you provide an example of calculating time when velocity is equal to 0 from a position vector?

Sure, let's say an object has a position vector of r = 3i + 4j, meaning it is located at the point (3,4) in a two-dimensional space. If the object's velocity is 0, we can use the formula t = (xf - xi)/v to calculate the time. Let's say the final position is (6,8), then the time would be t = ((6-3)i + (8-4)j)/0 = 3i + 4j/0. Since the object's velocity is 0, we cannot divide by 0 and therefore the time is undefined.

Similar threads

Calculating total Coulomb force vector ?
    • Introductory Physics Homework Help
Replies
1
Views
1K
Kinematics, curvilinear motion (a couple of questions)
    • Introductory Physics Homework Help
Replies
30
Views
513
Find velocity-time equation from velocity-position equation
    • Introductory Physics Homework Help
Replies
11
Views
965
Finding the y-component of a velocity vector
    • Introductory Physics Homework Help
Replies
2
Views
1K
Calculating Velocity Vector of Object in 2D Space
    • Introductory Physics Homework Help
Replies
10
Views
1K
Initial Position Discrepancy Involving Fluid Resistance
    • Introductory Physics Homework Help
Replies
5
Views
898
Finding shortest distance between an observer and a moving object
    • Introductory Physics Homework Help
Replies
13
Views
748
Projectile Motion velocity vector Problem
    • Introductory Physics Homework Help
Replies
2
Views
1K
Finding the expression for the x-component of velocity (vectors?)
    • Introductory Physics Homework Help
Replies
2
Views
2K
How do I graph the position for this velocity-time graph?
    • Introductory Physics Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top