Question

A spaceship is moving in space with a velocity of 50 kms⁻¹. Its engine fires for 10 s, such that its velocity increases to 60 kms⁻¹. Calculate the total distance travelled by a spaceship in 1/2 minute, from the time of firing its engine

Answer 1

Initial velocity of spaceship = u = 50 kms⁻¹
u = 50 × 1000 ms⁻¹
u = 50000 ms⁻¹
Time = t= 10s
Final velocity of spaceship = v = 60 kms⁻¹
v = 60 × 1000 ms⁻¹ = 6000 ms⁻¹
Acceleration = a = ?

Case – I
Spaceship acceleration for first 10 S
v = u + at
60000 = 50000 + a (10)
10a = 60000 − 50000 = 10000
a = `10000/10` = 1000 ms⁻² or 1 kms⁻²
S = ut + `1/2` at²
S = `50000(10)+1/2(1000)(10)^2`
S = 500000 + 500 × 100
= 500000 + 50000 = 550000 m
= 550 km

Case – II
Spaceship moves with uniform velocity 60 kms⁻¹ for next 20 S
Distance covered = Uniform velocity × Time
= 60 × 20 = 1200 km
Total distance travelled by spaceship = 550 + 1200 = 1750 km.