# Differential Equation of a model rocket

## Homework Statement

Suppose that the acceleration of a model rocket is proportional to the difference between 100 ft/sec and the rocket's velocity. If it is initially at rest and its initial acceleration is 50 ft/sec2, how long will it take to accelerate to 80 ft/s?

## The Attempt at a Solution

I've tried to solve like this.
Vi=0 a=50ft/s^2 Vf=80ft/s

a=k(100-v)
50=k(100-0)
k=0.5

Sorry but that's all I know. I'm new to this topic. I hope you can guide me. Thank you so much.

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LCKurtz
Homework Helper
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## Homework Statement

Suppose that the acceleration of a model rocket is proportional to the difference between 100 ft/sec and the rocket's velocity. If it is initially at rest and its initial acceleration is 50 ft/sec2, how long will it take to accelerate to 80 ft/s?

## The Attempt at a Solution

I've tried to solve like this.
Vi=0 a=50ft/s^2 Vf=80ft/s

a=k(100-v)
50=k(100-0)
k=0.5

Sorry but that's all I know. I'm new to this topic. I hope you can guide me. Thank you so much.
Hello aqmal_12, welcome to PF. You have the k figured out but you need to get your differential equation written. Remember that acceleration and velocity can be expressed in terms of position s and its derivatives. So what does your equation

a = k(100-v)

become when you express it in terms of s and its derivatives? Once you have that written, you have to solve it using techniques you have learned so far.