Integration (displacement or position)

In summary, the conversation is about a problem with integration on the left side of an equation and the attempt at finding a solution involving variables such as mass, gravity, thrust, velocity, and acceleration. The problem involves integrating both sides of the equation and using known values to solve for unknown values. One person suggests trying to solve it without a certain transition, while the other person expresses uncertainty about that approach but encourages them to try it anyway.
  • #1
kieran1black2
23
0

Homework Statement


the trouble is in the integration on the left side (go straight o my answer down the bottom of the page)... please help me...

mg-u-kv=m*a

where (all constant)
m= mass= 3000
g=gravity=10
u=thrust=172000
k=30

v=velocity=variable
a=acceleration=variable


Homework Equations



accel=v*dv/ds=dv/dt=a

The Attempt at a Solution



30000-172000-30v = 3000*v*dv/ds
-142000-30v = 3000*v*dv/ds
-(142000+30v) = 3000*v*dv/ds
142000+30v = -3000*v*dv/ds
(142000+30v)/v*dv = -3000*ds
v/(142000+30v)*dv = -1/3000*ds

and then integrate both sides, this is where my calculus stops

i know the right side (-1/3000*ds) becomes -1/3000s + c
where
s= displacement or position and
c= constant
i have 2 scenarios

when s=0, v=1000
and what i need to find is when v=0 what is s?


so once i integrate the left side i sub those values in.
 
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  • #2
kieran1black2 said:
(142000+30v)/v*dv = -3000*ds
v/(142000+30v)*dv = -1/3000*ds

Are you sure about this transition?
 
  • #3
if you think you can do it without that transition... go for it... that's just how i interpreted the question
 

1. What is integration in terms of displacement or position?

Integration refers to the mathematical process of finding the area under a curve, which can also be interpreted as finding the displacement or position of an object. It involves summing up small changes in a variable over a given interval to determine the total change or distance traveled.

2. What is the difference between integration and differentiation?

Integration and differentiation are inverse operations of each other. While integration involves finding the area under a curve, differentiation involves finding the slope of a curve at a specific point. In other words, integration deals with finding the total change while differentiation deals with finding the rate of change.

3. How is integration used in real-life applications?

Integration has a wide range of applications in various fields such as physics, engineering, economics, and statistics. For example, it is used to determine the displacement or velocity of objects in motion, to calculate the area or volume of irregular shapes, and to analyze data in finance and research studies.

4. What are the different methods of integration?

There are several methods of integration, including the basic technique of finding the antiderivative of a function, integration by parts, substitution, and partial fractions. These methods can be used to solve different types of integrals, depending on the complexity of the function.

5. What are some common mistakes to avoid when integrating?

One common mistake when integrating is forgetting to add the constant of integration. It is also important to pay attention to the limits of integration and to use the correct integration method for the given function. Additionally, it is crucial to check for algebraic errors and to use proper notation when writing the final answer.

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