Vectors, velocity in terms of unit vectors

In summary, the conversation discusses a particle moving in the xy plane with velocity components in the x and y directions. The equations for the displacement components x and y as functions of time are integrated, and the velocity and acceleration of the particle at a given time are calculated using initial vectors i and j. The magnitude of the acceleration and the time at which the velocity and acceleration are perpendicular are also determined.
  • #1
Vandella
25
0

Homework Statement



A particle moving in xy plane has velocity components in x and y directions
Dx/dt = b1+c1t and dy/dt = b2+c2t

A) integrate above equations to give displacement components x and y as functions of time
B) write the velocity (v) of the particle at time t in terms of initial vectors I and j
C) find acceleration a of the particle in terms of unit vectors I and j
D) write an expression for magnitude of acceleration
E) find an expression for the time at which v and a are perpendicular

I have integrated the equations to give x=b1t+(c1t^2)/2+ constant (x0)
And y=b2t+(c2t^2)/2+ constant (y0)

Do not know what to do next :/

Homework Equations





The Attempt at a Solution

 
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  • #2
Welcome to PF, Vandella! :smile:

The velocity is the vector (dx/dt, dy/dt), or written with i and j:
v=(dx/dt)i + (dy/dt)j.

To find the acceleration vector, you need to take the derivative.
 
  • #3
Thanks for the welcome :) and for the reply

I had written exactly what you had posted but had talked myself out of thinking it was correct and must be much more difficult
 
  • #4
I have to admit at being surprised that you could integrate the expressions and then not set up the vector for the velocity. :wink:

And as Occam's razor states: "The simplest explanation that fits all the facts is usually the right one!" :smile:
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is often represented by an arrow pointing in the direction of its motion.

2. What are the unit vectors?

Unit vectors are vectors with a magnitude of 1 and are used to indicate direction. The three unit vectors commonly used are the i, j, and k vectors, which represent the x, y, and z axes respectively.

3. How do you find the magnitude of a vector?

To find the magnitude of a vector, you can use the Pythagorean theorem by squaring the components of the vector, adding them together, and then taking the square root of the sum.

4. What is velocity in terms of unit vectors?

Velocity is the rate at which an object changes its position. In terms of unit vectors, it is represented by a vector with both magnitude (speed) and direction, with the unit vectors indicating the direction of motion.

5. How do you calculate the velocity of an object using unit vectors?

To calculate the velocity of an object using unit vectors, you need to first calculate the change in position or displacement (represented by a vector) over a certain time interval. Then, you can divide the displacement vector by the time interval to find the average velocity vector.

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