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.

Answer 1

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.