Graphs of acceleration, velocity, position

In summary, when finding the max velocity, acceleration, and position in a given function and interval, it is important to consider the direction of motion. Negative numbers may appear as the answer because they represent motion in the opposite direction, which can be greater in magnitude. This concept applies to 1-dimensional, 2-dimensional, and 3-dimensional space, as velocity and acceleration are vector quantities with both magnitude and direction.
  • #1
oneplusone
127
2
im confused with finding the max velocity , acceleration, and position.
Usually in these types of problems I'm given a function, and an interval and have to find the max acceleration or velocity.

Sometimes a negative number comes up which is greater in magnitude than the other numbers, and that is the answer. I don't get why. Can someone please explain?
Sorry if I'm being vague, i can't really explain it too well.
 
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  • #2
I don't see what would be special about a negative number. Negative and positive are arbitrary anyway, you could measure in the other direction and all signs would get swapped.
 
  • #3
Like mfb said, it's about directions.

Consider a horizontal line (which is 1-dimensional) and define a particular position, (i.e. point) as (0): all the positions (points) to the left of (0) will be negative, and all the positions (points) to the right of (0) will be positive.

  • A negative position will mean a position to the left of (0), a positive position will mean a position to the right of (0).
  • A negative velocity will mean motion to the left along the line, a positive velocity will mean motion to the right.
  • A negative acceleration will mean acceleration to the left along the line, a positive acceleration will mean acceleration to the right.
The same applies for 2-dimensional and 3-dimensional space too. Velocity and acceleration (and forces etc.) are vector quantities. Vectors have both magnitude and direction. See Euclidean vector.

See also:


A 2-D graph with velocity vectors (example):
Acceleration.JPG
 

1. What is the difference between acceleration, velocity, and position graphs?

Acceleration, velocity, and position graphs all relate to the motion of an object. Acceleration is the rate of change of velocity, velocity is the rate of change of position, and position is the location of the object at a given time. The main difference between these graphs is the variable being measured and how it changes over time. Acceleration is represented on the y-axis, velocity on the y-axis, and position on the x-axis.

2. How can I determine the acceleration of an object from its velocity graph?

To determine the acceleration from a velocity graph, you can look at the slope of the graph. The steeper the slope, the greater the acceleration. If the slope is positive, the acceleration is in the same direction as the velocity, and if the slope is negative, the acceleration is in the opposite direction.

3. What does a horizontal line on a position graph represent?

A horizontal line on a position graph represents a constant position, meaning the object is not moving. This can also be seen on a velocity graph as the line approaches zero, indicating a constant velocity of zero.

4. How can I determine the displacement of an object from its velocity graph?

To determine the displacement from a velocity graph, you can find the area under the curve. The displacement is equal to the change in position, which is represented by the area between the velocity line and the x-axis. This can be calculated using basic geometry or by using the trapezoidal rule.

5. Can an object have a changing acceleration but a constant velocity?

Yes, an object can have a changing acceleration but a constant velocity. This occurs when the acceleration and deceleration of the object cancel each other out, resulting in a constant velocity. This is commonly seen in objects moving in a circular path at a constant speed, as the direction of the velocity is constantly changing but the magnitude remains the same.

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