The coordinates of a bird flying in the xy plane are given by x(t)=?t and y(t)=3

Question

The coordinates of a bird flying in the xy plane are given by x(t)=?t and y(t)=3.0m??t2, where ?=2.4m/s and ?=1.2m/s2. Part A 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. Part B 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. Part C Calculate the magnitude of the bird's velocity at t=2.0 s. Express your answer using two significant figures. Part 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 using two significant figures Part E Calculate the magnitude of the bird's acceleration at t=2.0 s. Express your answer using two significant figures. Part F Calculate the direction of the bird's acceleration at t=2.0 s. Part G At t=2.0 s, is the bird speeding up, slowing down or moving at constant speed? At , is the bird speeding up, slowing down or moving at constant speed? speeding up ? or slowing down? or moving at constant speed?

Explanation / Answer

velocity = dx/ dt i + dy/dt j

= alpha i -2 tbetaj

a)sp velocity =(alpha, -2t beta) = (2.4, -2.4t)

b)acceleration = (0,-2.4)

c)magintude at (t = 2sec) =5.36m/sec ( sqrt( 2.4^2 + 4.8^2)

d) angle = arctan(-4.8/2.4) = arctan(-2)= -63.43 deg

e)|acceleration| = 2.4m/sec^2 at all times

f) a = -2.4 j so it is in Negative y-direction at all times

g)Constant acceleration in the y direction which speeds up the bird.

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