Question

question 20 (1 point) saved
an object is moving with constant non - zero velocity in the + x axis. the position versus time graph of this object is
a horizontal straight line.
a vertical straight line.
a straight line making an angle with the time axis.
a parabolic curve.
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Explanation:

To determine the position - time graph of an object moving with constant non - zero velocity along the +x axis, we start with the equation of motion for position. The position \(x\) of an object as a function of time \(t\) when it has a constant velocity \(v\) (and initial position \(x_0\)) is given by the equation \(x=x_0 + vt\). This is a linear equation in the form \(y = mx + c\) (where in our case, \(y=x\), \(m = v\) (the slope, which is the velocity), \(x = t\), and \(c=x_0\) (the y - intercept, which is the initial position)).

• A horizontal straight line would correspond to a velocity of \(v = 0\) (since the slope of a horizontal line is 0), so this option is incorrect.
• A vertical straight line is not a valid graph for motion in terms of position - time because time is a continuous variable and a vertical line would imply an undefined time rate of change of position, which is not physical for motion with constant velocity.
• A parabolic curve would correspond to motion with constant acceleration (the equation for position in that case is \(x=x_0+v_0t+\frac{1}{2}at^2\), which is a quadratic equation), so this option is incorrect.
• Since \(x=x_0 + vt\) is a linear equation, the graph of \(x\) versus \(t\) will be a straight line. The slope of this line is equal to the velocity \(v\). Since the velocity \(v\) is non - zero, the line will make an angle with the time (t) axis.

Answer:

a straight line making an angle with the time axis.