# Need clarification about x-t and v-t graph

1. Sep 4, 2010

### mizzy

1. The problem statement, all variables and given/known data
I'm confused with what a negative slope means on an x-t and v-t graph.

On an x-t graph, I understand that a positive constant slope means uniform velocity and when the slope is 0, then the object is stationary. On a v-t graph, constant slope means constant acceleration and a zero slope means constant speed.

What does the negative slope mean? is the object slowing down?

2. Relevant equations

3. The attempt at a solution

2. Sep 4, 2010

On an x vs. t graph:

If the slope is positive, then the velocity is constant and positive.
If the slope is zero, then velocity is zero.
If the slope is negative, then velocity is constant and negative.

On a v vs. t graph:

If the slope is positive, then the acceleration is constant and positive.
If the slope is zero, then the acceleration is zero.
If the slope is negative, then the acceleration is constant and negative.

Generally speaking, acceleration is the derivative of the equation for velocity with respect to time (a = dv/dt), and velocity is the derivative of the equation for position (v = dx/dt).

Hope that helps.

3. Sep 4, 2010

### mplayer

Linear negative slope on a x-t graph means uniform negative velocity. The object is moving in the opposite direction.

Linear negative slope on a v-t graph means constant deceleration. Or said in another way, constant negative acceleration.

4. Sep 4, 2010

### mizzy

but does it mean that the object is slowing down?

5. Sep 4, 2010

Depends. If acceleration and velocity are both the same sign (negative vs. positive), then it's speeding up. If the signs are different, it's slowing down. I think that's correct.

6. Sep 4, 2010

### mizzy

ok. so basically the negative or positive sign just tells us the direction and not if is speeds or slows down. correct??

i came across this question? If the average velocity of an object at a certain time interval is zero, what is its displacement? What's happening to the object?

If the average velocity is zero, the object is stationary. is that right?

7. Sep 4, 2010