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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 can you know if a graph represents a proportional relationship?
It is a relationship of direct proportion if and only if the graph is a straight line which passes through the origin. It is an inverse proportional relationship if the graph is a rectangular hyperbola. A typical example of an inverse proportions is the relationship between speed and the time taken for a journey.
What is a displacement time graph?
A displacement time graph is a graph that consists of an x and y axis using displacement, by time.
How do you get displacement from a displacement graph?
To get displacement from a displacement graph, just look at the Y- axis for the particular time (displacement versus time). For the displacement graph, the Y-axis is usually displacement.
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 equals the displacement on a velocity-time graph?
Displacement is the area under the v-t 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.
What does displacement divided by time give you?
The Average Velocity on a position time graph or a velocity time graph.
What is the condition of the position-time graph when the velocity-time graph passes through zero?
As, in the velocity-time graph, curves passes through zero means 'when time is zero velocity is zero'. Velocity is time derivative of displacement. So displacement is maximum or minimum when time is zero in position-time graph.
What variable is placed on the x axis in a displacement time graph?
It is time.
Velocity is the slope of a displacement vs time graph true or false?
False. The slope of a velocity vs time graph is acceleration
Can you tell from a displacemnt-time graph wheather an object is stationary?
Of course yes. An object is stationary when the graph is horizontal in a displacement-time graph.
Does a steep slope on a displacement vs time graph indicates a very large velocity?
Yes it does. Velocity = Displacement / Time. On a graph of displacement vs time, the slope is the velocity. Steeper slope = higher velocity, flatter slope = lower velocity.
