# Relationship of distance vs time

### Relationship between Speed, Distance and Time | Uniform Speed | Variable speed

Lesson 3 focuses on the use of position vs. time graphs to describe motion. of the relationship between the shape of a p-t graph and the motion of the object. Freefall occurs where the only force acting on an object is gravity. Because gravitational acceleration on earth is constant, the distance an object falls is proportional to the time spent falling. In this experiment, you will experimentally determine the acceleration due to. In a physics equation, given a constant acceleration and the change in velocity of an object, you can figure out both the time involved and the distance traveled.

## The Meaning of Shape for a p-t Graph

When objects are in true free fall, they will eventually reach their terminal velocity when the downward force from gravity and the upward force from air resistance are equal. A good anaology would be a skydiver: In this experiment, air resistance and drag are not really an issue because the objects fall very short distances.

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### Distance Speed Time Formula

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For further information, consult your state's handbook of Science Safety. Related learning resources Science project Distance, Velocity and Time: I'm just going to draw the magnitude of the velocity, and this right over here is my time axis. So this is time. And let me mark some stuff off here. So one, two, three, four, five, six, seven, eight, nine, ten. And one, two, three, four, five, six, seven, eight, nine, ten. And the magnitude of velocity is going to be measured in meters per second.

And the time is going to be measured in seconds. So my initial velocity, or I could say the magnitude of my initial velocity-- so just my initial speed, you could say, this is just a fancy way of saying my initial speed is zero. So my initial speed is zero. So after one second what's going to happen? After one second I'm going one meter per second faster.

So now I'm going one meter per second. After two seconds, whats happened?

Well now I'm going another meter per second faster than that. After another second-- if I go forward in time, if change in time is one second, then I'm going a second faster than that. And if you remember the idea of the slope from your algebra one class, that's exactly what the acceleration is in this diagram right over here.

The acceleration, we know that acceleration is equal to change in velocity over change in time. Over here change in time is along the x-axis. So this right over here is a change in time. And this right over here is a change in velocity. When we plot velocity or the magnitude of velocity relative to time, the slope of that line is the acceleration.

And since we're assuming the acceleration is constant, we have a constant slope.

So we have just a line here. We don't have a curve. Now what I want to do is think about a situation.

### Relationship Between the Distance and Time of a Falling Object | Science project | hidden-facts.info

Let's say that we accelerate it one meter per second squared. And we do it for-- so the change in time is going to be five seconds. And my question to you is how far have we traveled?

Which is a slightly more interesting question than what we've been asking so far.

## Why distance is area under velocity-time line

So we start off with an initial velocity of zero. And then for five seconds we accelerate it one meter per second squared. So one, two, three, four, five. So this is where we go. This is where we are. So after five seconds, we know our velocity. Our velocity is now five meters per second. But how far have we traveled?

So we could think about it a little bit visually. We could say, look, we could try to draw rectangles over here. This is an example of negative acceleration - moving in the negative direction and speeding up.

The graph on the right also depicts an object with negative velocity since there is a negative slope. The object begins with a high velocity the slope is initially large and finishes with a small velocity since the slope becomes smaller.

So this object is moving in the negative direction and slowing down. This is an example of positive acceleration. Negative - Velocity Leftward - Velocity Fast to Slow The principle of slope is an incredibly useful principle for extracting relevant information about the motion of objects as described by their position vs. Once you've practiced the principle a few times, it becomes a very natural means of analyzing position-time graphs.

The widget below plots the position-time plot for an object with specified characteristics. The top widget plots the motion for an object moving with a constant velocity. The bottom wideget plots the motion for an accelerating object. Simply enter the specified values and the widget then plots the line with position on the vertical axis and time on the horizontal axis.