A race car moves such that its position fits the relationshipx= (5.0 m/s)t + (0.75 m/s3)t3where x is measured in meters and t in seconds.(a) Plot a graph of the car’s position versus time.
Question
A race car moves such that its position fits the relationshipx= (5.0 m/s)t + (0.75 m/s3)t3where x is measured in meters and t in seconds.(a) Plot a graph of the car’s position versus time.
Solution
As an AI text-based model, I'm unable to plot graphs. However, I can guide you on how to do it:
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First, you need to understand the equation given. The equation x = (5.0 m/s)t + (0.75 m/s^3)t^3 is a third-degree polynomial equation, where x is the position of the car at time t.
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Choose a range of time values (t) for which you want to plot the position (x). For example, you can choose t values ranging from 0 to 10 seconds.
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For each chosen time value, calculate the corresponding position using the given equation. For example, if t=1 second, then x = (5.0 m/s)*1 + (0.75 m/s^3)*1^3 = 5.75 meters.
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Once you have a set of (t, x) pairs, you can plot them on a graph. The time values will be on the x-axis and the position values will be on the y-axis.
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Connect the points to see the trajectory of the car's movement over time. The shape of the graph will be a curve due to the cubic term in the equation.
Remember, the graph will show how the car's position changes with time according to the given equation.
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