Particle Motion with Constant Acceleration

In summary, the particle moves with constant acceleration from its starting point to its final destination. Its velocity changes from initial to final values.
  • #1
Loppyfoot
194
0

Homework Statement


A particle moves in the xy plane with constant acceleration. At t = 0 the particle is at rvec1 = (3.7 m)i + (3.4 m)j, with velocity vvec1. At t = 3 s, the particle has moved to rvec2 = (9 m)i − (1.9 m)j and its velocity has changed to vvec2 = (5.4 m/s)i − (6.5 m/s)j. (a) Find vvec1.(b) What is the acceleration of the particle?(c) What is the velocity of the particle as a function of time?(d) What is the position vector of the particle as a function of time?

I need some guidance. I tried using the average velocity formula for (a), but it doesn't seem to be working for me. I tried doing 9-3.7 / 3. for the i vector. And likewise, for the j vector (-1.9-3.4)/3. I get 1.76i-1.76j, and it isn't correct.

I need some guidance on the others too. Thanks guys.
 
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  • #2
Jeez, I cannot seem to get this! I have been trying to get it all night.
 
  • #3
Hi Loppyfoot! :smile:

(use bold for vectors :wink:)
Loppyfoot said:
… I tried using the average velocity formula for (a), but it doesn't seem to be working for me.

Distance velocity and acceleration are all vectors, and so they add like vectors.

Try s = vt + (1/2)at2 :wink:
 
  • #4
How should I implement that equation into part a), if I do not know the acceleration vectors yet?
 
  • #5
Part of your problem description doesn't make sense to me.
Edit: Now it does make sense.
Loppyfoot said:
A particle moves in the xy plane with constant acceleration. At t = 0 the particle is at rvec1 = (3.7 m)i + (3.4 m)j, with velocity vvec1. At t = 3 s, the particle has moved to rvec2 = (9 m)i − (1.9 m)j and its velocity has changed to vvec2 = (5.4 m/s)i − (6.5 m/s)j.
Edit: Ignore the following.
This description says that the particle moves with constant acceleration. Later it says that the velocity has changed to ... If the acceleration is constant, the velocity can't change, since acceleration is the instantaneous rate of change of velocity with respect to time.
 
Last edited:
  • #6
If the acceleration is constant, doesn't that mean that the velocity is changing at a constant rate?
 
  • #7
Never mind. I take back what I said. I was thinking zero acceleration, not constant acceleration.
 
  • #8
I think I figured it out. I applied one of the 4 kinematic equations, and then I should be able to get the rest from there.

EDIT: I got a and b, but how would I go about getting c and d?
 
  • #9
For c, if you got b, use it to get the velocity. a = dv/dt, so you can integrate what you have for a to get v as a function of t. You'll get a constant (vector) of integration, but you know v(3), so should be able to figure out the constant.

For d, do essentially the same thing: v = ds/dt. Integrate that to get s and use the given information about s(0) to figure out this constant (vector) of integration. Does that make sense?
 

1. What is a position vector?

A position vector is a mathematical representation of the location of an object in a coordinate system. It consists of a magnitude and a direction, and is typically represented by an arrow pointing from the origin to the object's location.

2. How is a position vector different from a displacement vector?

A position vector represents the location of an object at a specific point in time, while a displacement vector represents the change in an object's position over a period of time. In other words, a displacement vector shows the distance and direction an object has moved, while a position vector shows where the object is currently located.

3. What is a velocity vector?

A velocity vector is a mathematical representation of an object's speed and direction of motion. It is represented by an arrow pointing in the direction of the object's motion, with the length of the arrow representing the object's speed.

4. How are position and velocity vectors related?

Position and velocity vectors are related in that the velocity vector is the derivative of the position vector with respect to time. This means that the velocity vector represents the rate of change of an object's position over time.

5. How are position and velocity vectors used in physics?

Position and velocity vectors are used in physics to describe the motion of objects in a coordinate system. They are essential in understanding the laws of motion and calculating the position, velocity, and acceleration of objects in various scenarios.

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