Question On Displacement - Velocity-Time Graph

In summary, when calculating displacement using a velocity-time graph, it does not matter if the particle starts with a non-zero velocity. The displacement is independent of the path taken and only depends on the initial and final positions. This can be determined using the equation v^2=u^2+2as, which in this case would give a displacement of 50m. The negative part of the graph should not be excluded and must be added to get the final result.
  • #1
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[SOLVED] Question On Displacement -- Velocity-Time Graph

When calculating displacement, if you have a graph that starts with a non zero velocity, do you calculate the area from zero still, or do you calculate only from where it starts?

For instance, a linear problem with a velocity starting at 20m/s 0s and goes to 30m/s 2s.

Do I go Area=1/2bh=1/2(30m/s-20m/s x 2s-0s)=10m and then.. this is the part, do I calculate the left over rectangle under it even though the velocity started at a non zero number? 20m/s x 2s=40m

40m+10m=50m, or does it just stay with where the linear velocity started (10m)?
 
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  • #2
Displacement is independent of the path taken.
It depends only on the initial and the final positions.

Using the equation.:

v^2=u^+2as

we get s= 50m

It does not matter if the particle started with a non zero velocity.You must include that part of the rectangle also for calculating the displacement.The negative part of the graph does not mean you have to reduce that from the final answer.It must be added to get the final Result.
 
  • #3
Thank you very much!
 

What is displacement?

Displacement is the distance and direction an object has moved from its starting point. It is a vector quantity, meaning it has both magnitude (distance) and direction.

How is displacement calculated?

Displacement is calculated by subtracting the initial position from the final position. This can be represented as Δx = xf - xi, where Δx is displacement, xf is the final position, and xi is the initial position.

What is a velocity-time graph?

A velocity-time graph is a graphical representation of an object's velocity over time. It plots the velocity on the y-axis and time on the x-axis, with the slope of the graph representing the object's acceleration.

How do you interpret a velocity-time graph?

The slope of a velocity-time graph represents the object's acceleration. A positive slope indicates a positive acceleration (speeding up), while a negative slope indicates a negative acceleration (slowing down). A horizontal line indicates a constant velocity, and a vertical line indicates a change in velocity.

How can you determine displacement from a velocity-time graph?

Displacement can be determined by finding the area under the velocity-time graph. The area under the graph represents the change in displacement over a given time interval. This can be calculated by breaking the graph into smaller shapes and using their respective formulas (such as rectangles for constant velocity and triangles for changes in velocity).

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