Question

a flat (horizontal) x-t line means:
moving backward
constant velocity
constant acceleration
at rest

Explanation:

In a position - time (x - t) graph, the slope of the line represents velocity. The formula for the slope of a line between two points \((t_1,x_1)\) and \((t_2,x_2)\) is \(m=\frac{x_2 - x_1}{t_2 - t_1}\), where \(m\) is the slope (velocity in this case). For a horizontal line, the change in position \(\Delta x=x_2 - x_1 = 0\) (since the \(y\) - value, which is position \(x\) here, does not change). So the velocity \(v=\frac{\Delta x}{\Delta t}=\frac{0}{\Delta t}=0\). If velocity is zero, the object is not changing its position with respect to time, which means it is at rest.

• "moving backward" would correspond to a negative slope (negative velocity) in an x - t graph.
• "constant velocity" would correspond to a straight line with a non - zero constant slope (not a horizontal line).
• "constant acceleration" would be represented by a curve in an x - t graph (since acceleration is the rate of change of velocity, and a changing velocity would lead to a changing slope).

Answer:

D. at rest