# When acceleration depends on the distance

• svkptr
In summary, the conversation is about finding the velocity and distance covered by a particle with an acceleration that depends on distance. The equation a = k*s+c is used, along with the knowledge that a = ds/st, to derive the equation v = k*s*t+s*t. However, there is uncertainty about how to treat s in this equation. The solution involves using the differential equation s''(t)=k*s(t)+c, which is a second order ODE similar to a harmonic oscillator.

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svkptr

## Homework Statement

i am trying to find out velocity at a point of time and distance covered by a particle whose acceleration (a) depends on distance (s). to start with let a = k*s+c were k and c are contants.

a= k*s+c
we know a=ds/st

## The Attempt at a Solution

a=k*s+c

(dv/dt)=k*s+c
or
v=k*s*t+s*t

but i know (s) is not to be treated as conatant... then what to do here?? please help
i cannot frame the differential equation

a = dv/dt = dv/ds ds/dt = dv/ds v

a(t)=v'(t)=s''(t). So s''(t)=k*s(t)+c. It's a second order ode. Like a harmonic oscillator.

## 1. How does acceleration change with distance?

Acceleration is directly proportional to the distance traveled. This means that as the distance increases, the acceleration also increases. In other words, the more distance an object covers in a given amount of time, the greater its acceleration will be.

## 2. What is the relationship between velocity and distance when acceleration depends on distance?

When acceleration depends on distance, the velocity of an object will also increase as the distance traveled increases. This is because velocity is the rate of change of distance, and when acceleration increases, so does the rate of change of distance.

## 3. How does the graph of acceleration vs. time look when acceleration depends on distance?

The graph of acceleration vs. time when acceleration depends on distance will be a curve rather than a straight line. This is because the acceleration is changing as time passes, resulting in a non-linear relationship between these two variables.

## 4. Can acceleration depend on distance in a uniform motion scenario?

No, acceleration cannot depend on distance in a uniform motion scenario. Uniform motion is defined as constant velocity, meaning that there is no change in speed or direction. Therefore, there is no change in distance over time, and thus acceleration cannot depend on distance in this scenario.

## 5. How does the formula for acceleration change when acceleration depends on distance?

The formula for acceleration remains the same (a = Δv/Δt) when acceleration depends on distance. However, the value for acceleration will change as it is directly related to the distance covered. This means that the acceleration value will increase as the distance traveled increases.

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