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A space craft flying in a straight course with a
velocity of 75 km s-1 fires its rocket motors for
6.0 s. At the end of this time, its speed is
120 km s-l in the same direction. Find : (i) the space
craft's average acceleration while the motors were
firing, (ii) the distance travelled by the space craft
in the first 10 s after the rocket motors were started,
the motors having been in action for only 6.0 S.
Ans. (i) 7.5 km s2, (ii) 1065 km
show the procedure
Answers
Use kinematic equations:
SUVAT
s-displacement, u-initial velocity, v-final velocity,a- acceleration, t-time
v=u + at
v2 = u2 + 2as
s=1/2(u+v)t
s=ut + 1/2at2
a)Calculate the average acceleration when the motors were firing:
av. acceleration = change in velocity = 120 - 75 = 45m/s = 7.5m/s2
time 6s 6s
therefore the average acceleration = 7.5km/s^2
b)Distance traveled after the rockets were fired:
- Find distance traveled during the 6s when the motors were firing:
t=6s, v=120 km/s, u=75km/s, a=7.5km/s2
s= 1/2(u+v)t
= 1/2(120+75)6
=1/2 x 195 x 6
= 585 km
-Find distance after the motors are fired:(the next 4 seconds to make it 10 seconds)
After the motors are fired, the craft moves with 120km/s speed
That means in 4s = 4 x 120
= 480km
add the distance traveled in the 10s = (585 + 480)km
= 1065km
Therefore the total distance traveled = 1065 km