What is the area under a speed vs time graph?
Actually, the area under a speed vs time graph is distance. The area under a velocity vs time graph is displacement. The difference lies in the fact that velocity and displacement are vector quantities, while speed and distance are scalar quantities.
How do you find the area under a time graph?
Finding area under a graph is the same as Integrating. So Integration of the first derivative of displacement is displacement itself. Likewise, the area under acceleration time graph will give you velocity. Velocity and acceleration are themselves the derivatives of some physical quantity and hence area under these gr Nothing.
What do the shaded regions on the velocity-time graph represent?
The diagram below shows three different velocity-time graphs; the shaded regions between the line and the time-axis represent the displacement during the stated time interval. The shaded area is representative of the displacement during from 0 seconds to 6 seconds.
Why is distance greater than displacement on a speed vs time graph?
Under a speed vs time graph, the area under the curve may be equal to displacement, but if at any one point a change in direction occurred, that would not be reflected in the speed value because speed is only concerned with the absolute value of change in position over time. Therefore, the distance may be greater than displacement.
What is the area under the graph of a speed-time graph?
The area under the speed-time graph is the distance the particle travels.
Why is area under speed-time graph distance?
The area under the velocity-time graph will give us the magnitude of the displacement. This is because of displacement = velocity × time. The area under the speed-time graph will give us the distance.
What does area under graph represent?
The area under the curve is the magnitude of the displacement, which is equal to the distance traveled (only for constant acceleration).
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Calculating the Area of a Rectangle
Now we will look at a few example computations of the area for each of the above geometric shapes. First consider the calculation of the area for a few rectangles. The solution for finding the area is shown for the first example below. The shaded rectangle on the velocity-time graph has a base of 6 s and a height of 30 m/s.
Calculating the Area of a Triangle
Now we will look at a few example computations of the area for a few triangles. The solution for finding the area is shown for the first example below. The shaded triangle on the velocity-time graph has a base of 4 seconds and a height of 40 m/s.
Calculating the Area of a Trapezoid
Finally we will look at a few example computations of the area for a few trapezoids. The solution for finding the area is shown for the first example below. The shaded trapezoid on the velocity-time graph has a base of 2 seconds and heights of 10 m/s (on the left side) and 30 m/s (on the right side).
Alternative Method for Trapezoids
An alternative means of determining the area of a trapezoid involves breaking the trapezoid into a triangle and a rectangle. The areas of the triangle and rectangle can be computed individually; the area of the trapezoid is then the sum of the areas of the triangle and the rectangle. This method is illustrated in the graphic below.
Investigate!
The widget below computes the area between the line on a velocity-time plot and the axes of the plot. This area is the displacement of the object. Use the widget to explore or simply to practice a few self-made problems.
We Would Like to Suggest ..
Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Two Stage Rocket Interactive.
What does the area of velocity time graph give you?
Area of velocity time graph will give you displacement as well as distance.
What does the slope of a velocity line tell us about the velocity?
It gives us distance. And the slope of the line tells us about the way the velocity is changing, acceleration.
What happens when velocity is positive for a while but then negative?
As for why the area under a velocity vs time graph is not distance, but rather displacement , consider what happens if velocity is positive for a while but then negative. Displacement will reflect that change in direction as the value will begin to decrease with a negative velocity, but since distance recognizes no direction, it continues to record in the positive direction.
Why is area under velocity time graph?
The area under velocity time graph gives displacement. This is because velocity is the first derivative of displacement. Finding area under a graph is the same as Integrating.
What does slope mean in physics?
What we have instead is a curve whose slope represents velocity. If the velocity is changing over time, then the slope at any point indicates the instantaneous velocity.
What is the area under the slope?
The area under the slope is velocity.
What is the formula for s = 1/2?
We get: s = 1/2 * v * t = Area of the entire graph.
