• Support PF! Buy your school textbooks, materials and every day products Here!

Vectors, velocity in terms of unit vectors

  • Thread starter Vandella
  • Start date
  • #1
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

 

Answers and Replies

  • #2
I like Serena
Homework Helper
6,577
176
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
25
0
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 like Serena
Homework Helper
6,577
176
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:
 

Related Threads on Vectors, velocity in terms of unit vectors

Replies
1
Views
961
Replies
9
Views
1K
Replies
5
Views
639
Replies
2
Views
3K
  • Last Post
Replies
9
Views
675
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
911
  • Last Post
Replies
13
Views
2K
Replies
5
Views
1K
Top