Understanding Bidimensional Movement: A Homework Guide

[Jimmy84]

Homework Statement

I have this homework due for tomorrow and I am a bit stressed about it I really would appreciate some help I don't understand the concepts involved.

A particle that in t = 0 is in the origin, moves in the xy plane with a velocity :
v=[(2.0m/s^2)t -(1.0m/s^3)t^2] x - [-2.0m/s]+(3.0m/s^2)t] y

-Calculate the aceleration at t=4 s . Draw the graph of a vs t

-What kind of motions does the particle has?

-If the particle lasted 10 s traveling what was its total displacement?

Homework Equations

The Attempt at a Solution

I already have the components of aceleration by derivating Vx and Vy
at t= 4s the aceleration i found was 6.71m/s squared
I have no clue about how to draw the graph of a vs t since a is given as unit vectors of x n y how can I plot it?

I would truly appreciate your time
Thanks in advance.

 

[Jimmy84]

Please any help

 

[gneill]

You could plot the magnitude of the acceleration versus time.

You could plot the x and y components of the acceleration versus time separately (separate graphs).

You could produce a 3D plot with time on the Z-axis (probably a bit over the top for this sort of problem!).

 

[Jimmy84]

You could plot the magnitude of the acceleration versus time.

You could plot the x and y components of the acceleration versus time separately (separate graphs).

You could produce a 3D plot with time on the Z-axis (probably a bit over the top for this sort of problem!).

thanks i ploted the ax n ay graphs

What kind of motions does the particle has?
my first idea is to try to find the displament vector of y n x by integration. then to use it to describe the motion of the particle when it goes to the direction -x n -y

I know the questions are vague but that is how they were given.

 

[gneill]

I'm not sure how to answer a vague question like that. I can plot the motion and see it, but I'm not sure what would constitute a definitive answer as to "what kind of motion the particle has". Mathematically the x-component is a combination of square and cubic terms in t, while the y-component has linear and square terms in t. The result is a sort of quick loop in the first quadrant into the fourth quadrant, followed by a prolonged exit down and to the left in the third quadrant. I don't know of an elegant summarizing term for this shape.

 

[Jimmy84]

thanks I appreciate it well that is what I have to deal with my physics teacher