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