# Understanding Trajectory Graphs

• mymabelline
In summary, the conversation discusses the differences between trajectory graphs and position vs. time graphs in terms of the information they provide. It is determined that the slope of the trajectory graph gives the direction of velocity, but not the actual velocity, and that the acceleration found on the graph is the rate of change in the direction of velocity. There is also confusion about the role of tangential velocity and how it relates to speed. The conversation ends with a summary of the equation for a trajectory graph and how it can be differentiated to find the velocity at a specific point.
mymabelline
Trajectory Graphs??

## Homework Statement

The trouble I'm having is with determining what information I can get from a trajectory graph and how that information differs from what I can find on a position vs. time graph. Is the acceleration I find just the rate of change in the direction of velocity? and is the tangental velocity equal to speed or do we just we use it to represent the direction of velocity?

## The Attempt at a Solution

The only thing that I think I know for sure is that the slope of the trajectory graph gives the direction of velocity, but not the actual velocity. But I don't know why that is true, my book does a horrible job of explaining that.

You trajectory graph will be of the form y=bx-ax2.

So if you differentiate w.r.t t. you will get dy/dt = (b-2ax)dx/dt

dy/dt and dx/dt are both velocities, so you will get a velocity for the gradient.

## What is a trajectory graph?

A trajectory graph is a visual representation of an object's motion over time. It shows the relationship between an object's position, velocity, and acceleration.

## How do you interpret a trajectory graph?

To interpret a trajectory graph, you need to look at the shape and slope of the line. A straight line indicates constant velocity, while a curved line indicates a changing velocity. The slope of the line represents the acceleration, with a steeper slope indicating a greater acceleration.

## What factors can affect the shape of a trajectory graph?

The shape of a trajectory graph can be affected by the initial velocity of the object, the presence of external forces such as friction or air resistance, and the mass of the object.

## How can trajectory graphs be used in real-life situations?

Trajectory graphs are commonly used in physics and engineering to analyze the motion of objects, such as projectiles, vehicles, and satellites. They can also be used in sports to track the movement of athletes, in aviation to plot flight paths, and in video games to create realistic animations.

## What are the limitations of trajectory graphs?

One limitation of trajectory graphs is that they assume a constant acceleration, which may not always be the case in real-life situations. They also do not take into account external factors, such as wind or air resistance, which can affect an object's motion. Additionally, they only show the overall motion of an object and do not provide details about its path or trajectory.

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