Calculate Position & Acceleration Vectors of Bird in xy-Plane

[Xtasy]

A bird flies in the xy-plane with a velocity vector given by v(vector) = (a-bt^2)(i-vector) + ct (j-vector) , with a= 2.4m/s, b=1.6m/s^3,c=4.0m/s^2. The positive y-direction is vertically upward. At t=0 the bird is at the origin.

Calculate the position vector of the bird as a function of time.
Express your answer in terms of a, b, and z. Write the vector r(t) in the form vector(r(t)x,r(t)y , , where the x and y components are separated by a comma.

Calculate the acceleration vector of the bird as a function of time. also in the form as stated above.

What is the bird's altitude (y-coordinate) as it flies over x=0 for the first time after t=0?

 

[Pyrrhus]

I see, good standard questions...

Let's see how you are tackling them!

 

[Xtasy]

Well, atiderviative will give me the position vector, but I don't know if I should plug in the values of a, b, etc. prior to me taking the antiderivative. Also I am not sure what form they are talking about.

For the acceleration the derivative is needed.

Not sure about the last question

 

[Pyrrhus]

a, b, c are constants.

For the last question look at the position function, what can you notice?

 

[Xtasy]

I notice that x=0, so there is no horizontal motion. What do they mean by birds altitude as it flies over x=0 after t=0, meaning whent t=1. Also so since x=0 I only focus on the y componet of the position vector, which is (ct^2)/2?

 

[Pyrrhus]

Look at the acceleration vectorial function, it's x component is negative, so sooner or later the bird will pass the straight line x=0.