What type of motion is occurring when the slope of a position vs. time graph is constant?

Answer 1

It means the body is moving with constant velocity.

Answer 2

Though we're not here to do homework, consider what the graph is telling you...

You're comparing position (or say distance from a fixed point) to time.

So, let's say that you have a horizontal graph. We'll assume that time is on the X axis, and position is on the Y axis.

So, if the graph is horizontal, it means that the Y value isn't changing, so position isn't changing. It's sitting still.

Now, if the graph is a diagonal line, it means that as time changes, position changes too.
If the slope is downward from upper left to lower right, it means that as time advances to the right the position (or distance from a fixed point) is decreasing. In layman's terms, the object whose distance we're measuing from a fixed point is getting closer to the fixed point.
Likewise, if the diagonal is sloping upward from lower left, to upper right, what is happening? The opposite process. Distance is increasing from the fixed point as time proceeds to the right.

Now, if the slope of the line is "changing" that means that the speed at which the object is travelling isn't constant, since it's not a straight line. So, likely it's either a series of straight lines, OR it's a curve.

So, what happens if we plot a curve. Well, at any one point, the line tangent to the curve (touching/intersection in only one place on the curve) tells us the slope (I'm guessing you're probably not there yet in math, so I won't go into detail). But basically, what we'reseeign is a change in the RATE at which something is moving toward or away from a fixed point. So, we're seeing either acceleration or deceleration.

How to visualize this? Well, consider different slopes: 1/2, 1/3, 4/9.

What do these tell us? Well, we generally use the rule "rise over run" for fractions-as-slope (I think, it's been awhile since I had to think in t hese terms, so forgive me if I messed it up and got it backward). So, it tells you how much to increment the y value by and how much to increment the x value for each time you measure whatever you're measuring.

What does this mean in the real world? Well, on a graph, 1/2 means that for ever 2 units of X, you add one unit of Y. So, assuming we start at the origin (0,0), our next measurement or approximation of the graph will be at (2,1). Let's jut say we're thinking in terms of seconds and "feet away." This approximates a graph of "for ever 2 seconds, it moves one foot" or dividing by 2 "every second, it moves by half a foot."

If we change the slope to 1/3, we're now approximating a change of one foot every 3 seconds instead of two. (so it's taking us longer to move the same distance; we're moving more slowly). Or to put it naother way, every 1 second we're moving 1/3 of a foot or .333 ... feet instead of .5 feet (1/2 foot).

If we change the slope to 4/9, we're saying that every 9 seconds, we're moving 4 feet. To compare that to the other two fractions/slopes, let's divide: we get .444 ... feet. So, we're moving FASTER than 1/3, but slower than 1/2 (somewhere in the middle).

So, if we're changing the slope at any point on the graph, we're changing the speed the object is moving relative to a fixed point. Make more sense now, I hope? Hopefully I haven't confused you completely. ;o]

Answer 3

A constant slope means that the speed is constant. The speed is indeed defined as the time derivative of the position: graphically speaking, that's represented by the slope of your time-position curve.

Answer 4

Were you asleep during these classes about velocity, distance and time and what these graphs mean? Or are you just stupid enough to think that if you get the answer right without understanding it that it's somehow mysteriously the same as knowledge?

Do your own homework, at least then you might exercise the pitifully few brain cells you appear to currently possess.

Answer 5

motion at a constant speed. You have no accelration.

If it has a constant slope of 0 then the object is stoped.

Answer 6

Constant velocity motion. The second derivative (acceleration) would be 0.

Answer 7

if it were time/distance graph the constant gradient means that the distance travelled per unit of time is equal...therefore constant speed. If it were a speed time graph this would represent constant acceleration or decelleration.