Graph of x vs. t in x = xo + vot + (1/2)at^2

Thread starter ramancer
Start date Jun 4, 2009
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In summary, the graph of x vs. t represents the displacement of an object over time, with the x-axis representing time and the y-axis representing displacement. It is related to the equation x = xo + vot + (1/2)at^2, where the slope of the line is equal to the initial velocity (vo) and the area under the curve is equal to the displacement (x). The initial position (xo) represents the starting point of the object on the graph. The slope of the line on the graph is equal to the object's initial velocity (vo), and the acceleration (a) affects the shape of the graph by changing the slope of the line.

Jun 4, 2009

ramancer

For the equation x = xo + vot + (1/2)at2, what does a graph of x versus t look like?

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Jun 4, 2009

Cyosis

Homework Helper

Have you ever seen the graph of a quadratic equation? Are you familiar with the word parabola?

Jun 4, 2009

Homework Helper

Gold Member

Try setting x₀ = v₀ = 0 first. Does the resulting equation look familiar? What does it's graph look like?

FAQ: Graph of x vs. t in x = xo + vot + (1/2)at^2

What does the graph of x vs. t represent?

The graph of x vs. t represents the displacement of an object over time, where x is the displacement and t is the time.

How is the graph of x vs. t related to the equation x = xo + vot + (1/2)at^2?

The graph of x vs. t is a visual representation of the equation x = xo + vot + (1/2)at^2. The x-axis represents time and the y-axis represents the displacement. The slope of the line on the graph is equal to the initial velocity (vo) and the area under the curve is equal to the displacement (x).

What does the initial position (xo) represent on the graph of x vs. t?

The initial position (xo) represents the starting point of the object on the graph. It is the value of x at t=0.

How is the slope of the line on the graph related to the object's initial velocity?

The slope of the line on the graph is equal to the object's initial velocity (vo). This means that for every second that passes, the object's displacement increases by the initial velocity value.

How does the acceleration (a) affect the shape of the graph of x vs. t?

The acceleration (a) affects the shape of the graph of x vs. t by changing the slope of the line. If the acceleration is positive, the slope of the line will increase, resulting in a steeper curve. If the acceleration is negative, the slope of the line will decrease, resulting in a flatter curve.