# Homework Help: Straight-line graph

1. Apr 15, 2005

### 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 travelled 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.

2. Apr 15, 2005

### SpaceTiger

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

3. Apr 15, 2005

### recon

x = at(t) + 0.5 at2
= 1.5 at2 ???

This does not seem right.

4. Apr 15, 2005

### SpaceTiger

Staff Emeritus
Have you ever seen the formula:

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