Straight-Line Graph: x/t2 and t or x/t Pairs for Plotting

[recon]

A stone slides across an icy surface and travels a distance of x in time t while suffering uniform retardation. Which of the following pairs of quantities, plotted to represent the motion of the stone, would give a straight-line graph?

A. x and t
B. x and t²
C. x/t and t²
D. x/t and t
E. x/t² and t

This is my approach to the problem:

The initial velocity, u = at.

Hence, the distance traveled by the stone, x = 0.5at²

x/t² = (0.5at²)/t²

= 0.5a

Since a is a constant, then a flat line would be represented in a graph of axes x/t² and t.

Also, in D., x/t = v, which decreases at a constant rate because of the constant deceleration, so this is another straight-line graph.

Obviously, there must be something wrong with my reasoning because there can only be one, and not two answers for each multiple choice question.

 

[SpaceTiger]

The initial velocity, u = at.

Hence, the distance traveled by the stone, x = 0.5at²

Are you sure that's the full equation for position as a function of time? What about the initial velocity?

 

[recon]

x = at(t) + 0.5 at²
= 1.5 at² ?

This does not seem right.

 

[SpaceTiger]

Have you ever seen the formula:

$$x=v_0t+\frac{1}{2}at^2$$