Question

A spaceship travelling in space at 300 km s$^{–1}$, fires it's engine for 15 seconds, such that its final velocity is 600 km s$^{–1}$. Calculate the total distance travelled by the ship in one minute starting from the time of firing.​ solve fast​

Answer 1

Given:-

• Initial Velocity of Spaceship = 300km/s

• Final Velocity of Spaceship = 600km/s

• Time taken for Firing = 15s

• Total time given = 1min → 60s

To Find:-

The Total Distance travelled by the ship in one minute.

Formulae used:-

• v = u + at

• s = ut + ½ × a × t²

• s² = vt

Now,

we will find the Acceleration with which it was firing.

→ v = u + at

→ 600 = 300 + a × 15

→ 600 - 300 = 15a

→ 300 = 15a

→ a = 300/15

→ a = 20km/s

→ a = 20000m/s

Now, we will find the Distance travelled while firing

→ s¹ = ut + ½ × a × t²

→ s = 300000 × 15 + ½ × 20000 × (15)²

→ s = 4500000 + 10000 × 225

→ s = 4500000 + 225000

→ s = 6750000

Therefore, S¹ = 4725000

Now,

→ t = 60 - 15 → 45

→ after travelling for 15s the Velocity of the spaceship will be uniform.

Therefore,

→ s² = ut

→ s² = 600000 × 45

→ s² = 27000000

Hence,

→ Total Distance travelled = s¹ + s²

→ 6750000 + 27000000

→ 33750000

→ 33750km.

Hence, total distance travelled by spaceship is 31725km.

Answer 2

Answer:

Given that:

Spaceship travelling in space at 300 km s$^{–1}$ fires it's engine for 15 seconds.

To find:

Total distance travelled by the ship in one minute.

Solution:

In case 1: when the spaceship is accelerating:

It's initial velocity (u) = 300 km s$^{–1}$

Final velocity (v) = 600 km s$^{–1}$

And Time (t) = 15s.

Using first equation of motion

v = u + at

$\Longrightarrow$ 600 = 300 + a × 15

$\Longrightarrow$ 600 = 300 + 15 a

$\Longrightarrow$ 15 a = 300

$\Longrightarrow$ a = 20 kms$^{–2}$

Now using second equation of motion

S = ut + 1/2at$^{2}$

$= 300 \times 15 + \frac{1}{2} \times 20 \times (15) {}^{2} \\ \\ = 4500 + 2250 = 6750 \: km.$

In case 2: When spaceship is moving with uniform velocity of 600 kms$^{–1}$ for next 45 s.

Distance covered = Uniform velocity × Time.

= 600 × 45 = 27000 km.

Therefore total distance travelled by spaceship in one minute.

= Distance travelled in first case and distance travelled in second case.

= 6750 + 27000

= 33,750 km.

Hence total distance travelled by spaceship in one minute is 33,750 km.

Equations of motion:-

• v = u + at
• S = ut + 1/2at$^{2}$
• v$^{2}$ – u$^{2}$ = 2as