Answer:
95.78125%
18000 m/s
22233.33 seconds
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
[tex]v=u+at\\\Rightarrow v=0+20\times 15\times 60\\\Rightarrow v=18000\ m/s[/tex]
The velocity of the rocket at the end of the first 15 minutes is 18000 m/s which is the maximum speed of the rocket in the complete journey.
Distance traveled while speeding up
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 20\times 900^2\\\Rightarrow s=8100000\ m[/tex]
Distance traveled while slowing down
[tex]s=18000\times 900+\dfrac{1}{2}\times -20\times 900^2\\\Rightarrow s=8100000\ m[/tex]
Distance traveled during constant speed
[tex]384000000-(2\times 8100000)=367800000\ m[/tex]
Fraction
[tex]\dfrac{367800000}{384000000}\times 100=95.78125\ \%[/tex]
Fraction of the total distance is traveled at constant speed is 95.78125%
Time taken at constant speed
[tex]t=\dfrac{367800000}{18000}=20433.33\ s[/tex]
Total time taken is [tex]900+20433.33+900=22233.33\ s[/tex]