Finding acceleration from Velocity vs Position graph

In summary, the conversation discusses how the answer to a question was determined to be E instead of A, and the use of the chain rule in finding the derivative of a linear function to prove the answer. The conversation also rules out possible choices for the answer through the use of equations.
  • #1
iceninja3
6
4
Homework Statement
The velocity versus position plot of a particle is shown on the right. Which of the following choices is the correct acceleration vs position plot of the particle (picture attached)?
Relevant Equations
dv/dt = a
dx/dt = v
Screen Shot 2022-12-18 at 3.24.12 PM.png

The answer is E. I was initially very confused as to why the answer was not A but realized that the graph was velocity vs position (rather than velocity vs time) which means I can't simply take the derivative of the given graph.

One thing I tried was writing out the equation first(c being a constant):
v = cx
*differentiating both sides with respect to time*
a = c•(v) = (c^2)•x
So a constant times x which rules out choices B and D.

Having recognized that I am still not sure how to move forward to prove to myself the answer is E. Any hints?
 
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  • #2
Think about the velocity as a function of ##x## as a linear function:

$$v(x) = b + mx $$

You are going to use the chain rule to get ##\frac{dv}{ dt}##
 
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  • #3
erobz said:
Think about the velocity as a function of ##x## as a linear function:

$$v(x) = b + mx $$

You are going to use the chain rule to get ##\frac{dv}{ dt}##
Ohhh I see. So if I do the chain rule I would get:
a = mv and then substituting x back:
a = m(mx+b)
a = m^2x + mb
m^2x + mb rules out B and D because x is linear. And rules out C because the y-intercept is nonzero. And rules out A because the slope is nonzero.

Thank you so much!
 
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What is acceleration?

Acceleration is the rate of change of velocity over time. It is a vector quantity, meaning it has both magnitude and direction. It is commonly measured in meters per second squared (m/s^2).

How is acceleration related to velocity and position?

Acceleration is the second derivative of position, meaning it is calculated by taking the rate of change of velocity over time. This means that acceleration is directly related to both velocity and position.

How can I find acceleration from a Velocity vs Position graph?

To find acceleration from a Velocity vs Position graph, you can calculate the slope of the line at any given point. The slope at a specific point represents the instantaneous acceleration at that point. You can also find the average acceleration by calculating the slope of the line between two points on the graph.

What units are used to measure acceleration?

Acceleration is commonly measured in meters per second squared (m/s^2). However, depending on the context, it can also be measured in other units such as feet per second squared (ft/s^2) or kilometers per hour squared (km/h^2).

What factors can affect the acceleration of an object?

The acceleration of an object can be affected by various factors, including the net force acting on the object, its mass, and the presence of any external forces such as friction or air resistance. The direction of the net force also plays a role in determining the direction of acceleration.

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