#1) A bird, initially at rest, begins flying horizontally at time t=0. The birds
ID: 584437 • Letter: #
Question
#1) A bird, initially at rest, begins flying horizontally at time t=0. The birds velocity as a function of time once it begins flight is given by v(t)=(1.25 m/s^2)t-(1.5/pi m/s)sin[(pi rad/s)t]
a) Find the position of the bird as a function of time. Assume x=0 is the initial location of the bird when it begins flight.
b)Find the acceleration of the bird as a function of time.
c)Find the maximum acceleration of the bird during its flight.
If you can show work of how you solved this problem I'D greatly appreciate it. Thank you.
Explanation / Answer
v(t)=(1.25)t - (1.5/pi) * sin[(pi)t]
Distance = Velovity *time
ds = v(t).dt
ds = [(1.25)t - (1.5/pi) * sin[(pi)t] ].dt
s = 1.25*t^2/2 - (1.5/pi) * cos[(pi)*t] * (1/pi)
s = 0.625 t^2 - 0.151982*cos(pi*t)
Position of the bird as a function of time, s = 0.625 t^2 - 0.151982*cos(pi*t)
(b)
Acceleration = Velocity/time
a = dv/dt
a = d/dt * {(1.25)t - (1.5/pi) * sin[(pi)t]}
a = 1.25 - 1.5 * cos(pi*t)
Acceleration of the bird as a function of time, a = 1.25 - 1.5 * cos(pi*t)
(c)
For Max acceleration,
da/dt = 0
0 + 1.5*sin(pi*t) = 0
sin(pi*t) = sin(pi)
t = 0,1,2
At t = 1
a = 1.25 - 1.5 * cos(pi*1)
a = 1.25 + 1.5 m/s^2
a = 2.75 m/s^2
Max acceleration, a = 2.75 m/s^2
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