Set up a proportion
1 mile/1.6 km = 20,000miles/x
Cross Multiply
x = (20,000) * (1.6)
x = 32,000 kilometers
Answer
given,
x = (3.9 cm)sin[(9.3 rad/s)πt]
general equation of displacement
x = A sin ω t
A is amplitude
now on comparing
c) Amplitude =3.9 cm
a) frequency =


f = 4.65 Hz
b) period of motion


T = 0.215 s
d) time when displacement is equal to x= 2.6 cm
x = (3.9 cm)sin[(9.3 rad/s)πt]
2.6 = (3.9 cm)sin[(9.3 rad/s)πt]
sin[(9.3 rad/s)πt] = 0.667
9.3 π t = 0.73
t = 0.025 s
Magnitude of acceleration = (change of speed) / (time for the change)
Change of speed = (speed at the end) - (speed at the start)
Change of speed = (18 m/s) - (0 m/s) = 18 m/s
Time for the change = 22 sec
Magnitude of acceleration = (18 m/s) / (22 sec)
<em>Magnitude of acceleration = 0.818 m/s²</em>