Equation for Final Position and Distance on a Velocity vs Time Graph

In summary, on a velocity vs time graph, the equation to find final position is \dot{y} = \dot{y}(0) + at. To find the distance traveled on the same graph from 4 seconds to 15 seconds, use the equation \int_{4}^{15}\,v(t)\,dt, where v(t) is the velocity and t is the time. This assumes no acceleration and that the velocity is given by v(t) = dx(t)/dt.
  • #1
Drewser
2
0

Homework Statement


Do you know the equation to find final position on a velocity vs time graph

Plus on the same graph how do you find the distance traveled, equation wise too from 4 seconds to 15 seconds?


Homework Equations



No idea

The Attempt at a Solution



22 meters but all I need are the equations
 
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  • #2
No, you don't need any magic equations. Is your graph of velocity a straight slope? Would you know how to find an equation from a graph with y = mx + b?

Don't just ask for equations without any work or thoughts about anything because I might as well assume you could solve this
[tex] \dot{y} = \dot{y}(0) + at[/tex]
 
  • #3
Is this in one dimension?

if velocity is given by v(t) = dx(t)/dt, then distance traveled in time interval between ti and tf is given by

[tex]\int_{t_i}^{t_f}\,v(t)\,dt[/tex]

where ti is the initial time and tf is the final time.

This assumes no acceleration.
 

1. What is final position?

Final position refers to the location or placement of an object or person at the end of a given time or event.

2. How is final position calculated?

Final position can be calculated by determining the distance an object or person has traveled from their starting point and in which direction, using a reference point or coordinate system. This can be done using mathematical equations such as displacement or vector addition.

3. What factors influence final position?

The factors that influence final position can include the initial position, velocity, acceleration, and any external forces acting on the object or person. These factors can change the direction and speed of movement, ultimately determining the final position.

4. Why is final position important in scientific research?

Final position is important in scientific research because it helps to understand and analyze the movement and behavior of objects and people. It can also be used to predict future positions and make calculations for various experiments and studies.

5. How can final position be represented graphically?

Final position can be represented graphically using a coordinate system, such as a Cartesian plane, where the final position is plotted as a point on the graph. It can also be represented using vector diagrams, where the final position is shown as an arrow with magnitude and direction.

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