How Long Should Pilots Fire Engines for Safe Re-entry?

[pkhor]

For a safe re-entry into the Earth's atmosphere, the pilots of a space capsule must reduce their speed from 2.6 x 10^4 m/s to 1.1 x 10^4 m/s. The rocket engine produces a backward force on the capsule of 1.8 x 10^5 N. The mass of the capsule is 3800 kg. For how long must they fire their engine? [Hint: Ignore the change in mass of the capsule due to the expulsion of exhaust gases.]

The answer to this problem is 320 seconds, but I have no idea how to get to that answer. I just want to know the formula or theorem that I can use to solve this specific problem. Your help would be highly appreciate.

PS. sorry for my English, I'm not a native speaker.

 

[Pyrrhus]

Newton's 2nd Law

$$\sum_{i=1}^{n} \vec{F}_{i} = \frac{d \vec{P}}{dt}$$

Using $\vec{p} = m \vec{v}$

$$\sum_{i=1}^{n} \vec{F}_{i} = \frac{d (m \vec{v})}{dt}$$

The problem states mass is constant therefore it can go out of the derivative.

$$\sum_{i=1}^{n} \vec{F}_{i} = m \frac{d\vec{v}}{dt}$$

For Finitessimals:

$$\sum_{i=1}^{n} \vec{F}_{i} = m \frac{\Delta \vec{v}}{\Delta t}$$

 

[pkhor]

My course is Algebra based physics.
I can't understand Calculus, so is there any formula that based on algebra?
Thanks for your respond.

 

[KnowledgeIsPower]

For a safe re-entry into the Earth's atmosphere, the pilots of a space capsule must reduce their speed from 2.6 x 10^4 m/s to 1.1 x 10^4 m/s. The rocket engine produces a backward force on the capsule of 1.8 x 10^5 N. The mass of the capsule is 3800 kg. For how long must they fire their engine? [Hint: Ignore the change in mass of the capsule due to the expulsion of exhaust gases.]

Use F=Ma to find the acceleration due to the backward force. You can then find the time needed to reduce their speed to the correct value.

 

[maxwellwest]

This problem involves manipulating the impulse-momentum theorem.
We know that Impulse is equal to the change in momentum (I=Δp) where change in momentum is Δp=mv(final)-mv(initial). We also know that Impulse is equal to Force*change in time (I=FΔt). Using these formulas you should be able to solve this question with ease.