# Vectors, velocity in terms of unit vectors

Vandella

## 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 :/

## The Attempt at a Solution

Homework Helper
MHB
Welcome to PF, Vandella!

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.

Vandella
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

Homework Helper
MHB
I have to admit at being surprised that you could integrate the expressions and then not set up the vector for the velocity.

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