I am struggling to solve 3 parts. please help. thanks! The coordinates of a bird

Question

I am struggling to solve 3 parts. please help. thanks!

The coordinates of a bird flying in the xy plane are given by x(t) = alpha(t) and y(t) = 3.0m - beta t2, where alpha = 2.4 m/s and beta = 1.2 m/s2. Calculate the velocity vector of the bird as a function of time. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3t and the y component is 4t, then you should enter 3t, 4t. Express your answer using two significant figures for all coefficients. Calculate the acceleration vector of the bird as a function of time. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3t and the y component is 4t, then you should enter 3t, 4t. Express your answer using two significant figures for all coefficients. Calculate the magnitude of the bird's acceleration at t = 2.0 s. Express your answer using two significant figures.

Explanation / Answer

PART A

Vx=dx/dt=d(alpha *t)/dt=alpha

Vy=dy/dt=d(3-beta*t^2)/dt=-2*beta*t............[derivative of constant is 0,derivative of t^2 w.r.t. t is 2t]

answer: alpha,-2*beta*t

PART B

Ax=dVx/dt=d(alpha)/dt=0

Ay=dVy/dt=d(-2*beta*t)/dt=-2*beta

answer:0,-2*beta

PART C

Ax=0

Ay=-2*1.2=-2.40 m/s^2 ...........[doesnt depend on time,only on beta]

magnitude=root(0^2+(-2.4)^2)=2.4 m/s^2

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