# Relationship of distance and time in terms speed

### Speed & Velocity – The Physics Hypertextbook Given that time in all likelihood is solely a human notion with no material existence The relation between time and speed is that speed is the amount of distance definition, |dr/dt|=|v|, where r is position, v is velocity, |v| is speed, and t is time. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time. Contrast this to a slow-moving object that has a low speed. where d is distance traveled in a certain amount of time (t), v is starting velocity, A constant force applied to an object which reaches relativistic speeds, so that Addendum- I'd left out the expression for distance h in terms of time, t, thinking it.

• Speed & Velocity
• Distance Speed Time Formula
• Why distance is area under velocity-time line

That's the velocity, let me color-code this. That is the velocity. And we know what the change in time is, it is five seconds.

### BBC - GCSE Bitesize: Speed, distance and time

And so you get the seconds cancel out the seconds, you get five times five-- 25 meters-- is equal to 25 meters. And that's pretty straightforward. But the slightly more interesting thing is that's exactly the area under this rectangle right over here. What I'm going to show you in this video, that is in general, if you plot velocity, the magnitude of velocity. So you could say speed to versus time. Or let me just stay with the magnitude of the velocity versus time. The area under that curve is going to be the distance traveled, because, or the displacement. Because displacement is just the velocity times the change in time. So if you just take out a rectangle right over there. So let me draw a slightly different one where the velocity is changing.

So let me draw a situation where you have a constant acceleration. The acceleration over here is going to be one meter per second, per second.

So one meter per second, squared. And let me draw the same type of graph, although this is going to look a little different now. So this is my velocity axis. I'll give myself a little bit more space. 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. 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. 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.

## Describing motion - AQA

Maybe right over here, we have the velocity of one meter per second. If you know any 3 of those things, you can plug them in to solve for the 4th.

So if you only know v and d, you can't solve for a unless you also know what t is i. The answer given to this question is incorrect. The original answer apparently assumed that the velocity you knew was only the initial one.

In that case that answer is correct as stands. You seem to assume we know both the initial and final velocities. So of course if you know two velocities you know more than if you just know one. In the formula for distance: How do you calculate for distance then?

You'll have to specify this a little more before we can answer. Is there constant acceleration until that velocity is reached, then the acceleration stops? If so, I bet you could solve it yourself. Or is there, more plausibly, one of these other situations which also lead to limiting velocities: This applies to objects whose terminal velocities correspond to small Reynold's numbers.

This applies to objects whose terminal velocities correspond to larger Reynold's numbers, including typical large falling objects. Some other effect not in the list? I think you're looking too much into my question. I don't understand what 'reynold's numbers' are. Or the time be if distance is given, but not time?