The coordinates of a bird flying in the xy plane are given by x(t)=αt and y(t)=3.0m−βt2, where α=2.4m/s and β=1.2m/s2.
a) Calculate the velocity vector of the bird as a function of time. (Express your answers in meters per second in terms of t separated by a comma.)
b) Calculate the acceleration vector of the bird as a function of time. (Express your answers in meters per second squared in terms of t separated by a comma.)
c) Calculate the magnitude of the bird's velocity at t=2.0 s . (Express your answer in meters per second.)
d) Let the direction be the angle that the vector makes with the +x axis measured counterclockwise. Calculate the direction of the bird's velocity at t=2.0 s . (Express your answer in degrees.)
e) Calculate the magnitude of the bird's acceleration at t=2.0 s . (Express your answer in meters per second squared.)
f) Calculate the direction of the bird's acceleration at t=2.0 s . (Express your answer in degrees.)
g) At t=2.0 s , is the bird speeding up, slowing down or moving at constant speed?