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Question
A space craft flying in a straight course with 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-1 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 being in action for only 6 s.
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Solution
Given, the initial velocity u = 75 km/s
Final velocity v = 120 km/s
Time taken = 6 s
(i) Acceleration = (Final velocity - Initial velocity)/time taken
= [(120 - 75)/6] kms-2
= (45/6) kms-2
= 7.5 kms-2
(ii) Distance travelled by the aircraft in the first 10 s = Distance travelled in the first 6 s + Distance travelled in the next 4 s.
Distance travelled in the first 6s (S1) = ut + (1/2) at2
(S1) = ut + (1/2) at2
(S1) = (75)(6) + (1/2) (7.5)(6)2
(S1) = 450 + 135
(S1) = 585 km
Distance travelled in the next 4 s (S2) = Speed × time
Speed at the end of 6 s is 120 km/s.
(S2) = (120) (4)
(S2) = 480 km
Thus, the distance travelled by the aircraft in the first 10 s = (S1) + (S2) = 585 + 480 = 1065 km.
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