- #1
Stephanus
- 1,316
- 104
Dear PF Forum,
How to use integral?
I created a thread months ago to find out what is the integral of Hubble equation.
Now, I create a thread to understand how to use the integral.
Problem 1:
Something is constantly accelerating 10m/s per meter. Let's say the acceleration is H.
so H = 10m . s-1. h-1
Velocity = H x Distance; V = HD
For a given distance, how can we find the time it takes to cover that distance?
Problem 2:
Something is constantly accelerating 10m/s per second. Let's say the acceleration is a
so a = 10 m.s-1.s-1
or a = 10 m/s2
For a given time, how can we find the distance it takes?
I know the answer is D = 1/2 at2. We were taught that at high school.
Instinctively it is the integral of D = VT
I'll try to make a sentence like RyanH42.
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##V = dx/dt## then ##dx = V dt## then integrate it ##V = a.t## inside the integral will be ##\int a.t \, dt##
--------------------------------------------------------------------------------------------------------------------------------------------
Is this sentence correct? I try to understand how to use the integral to solve a problem not to integrate an equation.
How to use integral?
I created a thread months ago to find out what is the integral of Hubble equation.
Now, I create a thread to understand how to use the integral.
Problem 1:
Something is constantly accelerating 10m/s per meter. Let's say the acceleration is H.
so H = 10m . s-1. h-1
Velocity = H x Distance; V = HD
For a given distance, how can we find the time it takes to cover that distance?
Someone has given me the answer. Okay..., I get it.RyanH42 said:##V=dx/dt## then ##dt=dx/V## then integrate it ##V=HD## İnside the integral will be ##1/H_0xdx##
Problem 2:
Something is constantly accelerating 10m/s per second. Let's say the acceleration is a
so a = 10 m.s-1.s-1
or a = 10 m/s2
For a given time, how can we find the distance it takes?
I know the answer is D = 1/2 at2. We were taught that at high school.
Instinctively it is the integral of D = VT
I'll try to make a sentence like RyanH42.
---------------------------------------------------------------------------------------------------------------------------------------------
##V = dx/dt## then ##dx = V dt## then integrate it ##V = a.t## inside the integral will be ##\int a.t \, dt##
--------------------------------------------------------------------------------------------------------------------------------------------
Is this sentence correct? I try to understand how to use the integral to solve a problem not to integrate an equation.