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.​

Answer 1

GIVEN :–

• Initial velocity (u) = 300 Km/s

• Final velocity (v) = 600 Km/s

• Time (t) = 15 second

TO FIND :–

• Travelled distance in one minute after fires it's engine ?

SOLUTION :–

• We know that –

$\\ \implies \bf v = u + at$

• Put the values –

$\\ \implies \bf 600= 300+ a(15)$

$\\ \implies \bf 600 - 300 = 15a$

$\\ \implies \bf 300 = 15a$

$\\ \implies \bf a = 20 \: Km/ {s}^{2}$

• So , Travelled Distance in 15 seconds –

$\\ \implies \bf S=ut +\dfrac{1}{2} a {t}^{2}$

$\\ \implies \bf S_1 =(300)(15)+\dfrac{1}{2} (20) {(15)}^{2}$

$\\ \implies \bf S_1 =4500+2250$

$\\ \implies \bf S_1 =6750$

• Travelled distance in next 45 sec with uniform speed (no acceleration) is –

$\\ \implies \bf S_2 =vt$

$\\ \implies \bf S_2 =(600)(45)$

$\\ \implies \bf S_2 =27000$

• Hence , Total travelled distance in one minute is –

$\\ \implies \bf S = S_1 + S_2$

$\\ \implies \bf S = 6750 + 27000$

$\\ \implies \large { \boxed{\bf S = 33750 \:\:Km}}$

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