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What does the displacement vs time graph look like for an object thrown downward from a cliff?
The displacement vs. time graph for an object thrown downward from a cliff is a curved line that starts at the initial height and slopes downward. As time progresses, the slope of the graph becomes steeper, reflecting the increasing speed of the object due to gravitational acceleration. The curve is concave upward, indicating that the object is accelerating as it falls. Overall, the graph illustrates a non-linear relationship between displacement and time.
What is calculus and what does it have to do with?
Calculus is a branch of mathematics which came from the thoughts of many different individuals. For example, the Greek scholar Archimedes (287-212 B.C.) calculated the areas and volumes of complex shapes. Isaac Newton further developed the notion of calculus. There are two branches of calculus which are: differential calculus and integral calculus. The former seeks to describe the magnitude of the instantaneous rate of change of a graph, this is called the derivative. For example: the derivative of a position vs. time graph is a velocity vs. time graph, this is because the rate of change of position is velocity. The latter seeks to describe the area covered by a graph and is called the integral. For example: the integral of a velocity vs. time graph is the total displacement. Calculus is useful because the world is rarely static; it is a dynamic and complex place. Calculus is used to model real-world situations, or to extrapolate the change of variables.
What physical property does the slope of a velocity time graph represent?
velocity.
How do you calculate the distance in the s-t graph?
The distance covered between two points in time is the area under the graph between the two points.
What does the slope of the curve on a velocity time graph represent?
The rate of Change in acceleration.
How do you get displacement from a displacement graph?
To calculate displacement from a displacement graph, find the area under the curve. If the graph is a straight line, you can subtract the initial position from the final position. If the graph is not a straight line, calculate the integral of the graph to determine the total displacement.
What is a displacement time graph?
A displacement-time graph is a visual representation that shows how an object's position changes over time. The slope of the graph indicates the object's velocity, while the area under the graph corresponds to the total distance traveled by the object.
The slope of a displacement-time graph is?
The slope at each point of a displacement/time graph is the speed at that instant of time. (Not velocity.)
What is the gradient of a graph in a displacement time and velocity time graphs?
In a displacement-time graph, the gradient represents velocity. In a velocity-time graph, the gradient represents acceleration.
What equals the displacement on a velocity-time graph?
Displacement is the area under the v-t graph.
Is displacement the slope of the velocity vs time graph?
No, displacement is the area under the velocity vs. time graph. The slope of a velocity vs. time graph represents acceleration.
How can one calculate displacement from a position-time graph?
To calculate displacement from a position-time graph, find the difference between the initial and final positions on the graph. This difference represents the total displacement traveled by the object.
Is velocity the slope of the displacement vs time graph true or false?
True. Velocity is the rate of change of displacement with respect to time, which is represented by the slope of the displacement versus time graph.
How can you use graphs to find the displacement of an object?
You can use a position-time graph to find the displacement of an object by determining the change in position between the initial and final points on the graph. The displacement is the area under the curve of the graph, which corresponds to the distance traveled by the object in a particular time interval. Mathematically, displacement can be calculated by integrating the velocity-time graph or finding the slope of the graph at different time points.
How can you determine the displacement of an object from a velocity time graph?
The displacement of an object from a velocity-time graph can be determined by finding the area under the velocity-time graph. For example, the displacement over a certain time interval can be calculated by finding the area of the corresponding region under the velocity-time graph. This can be done by calculating the area of the trapezoid or rectangle formed by the graph.
What settings describe a displacement versus time graph?
Constant velocityZero acceleration and/or Moving object
Slope of a displacement time graph?
It is the instantaneous speed in the direction in which the displacement is measured.
