Relationship between distance time graph and velocity

What are velocity vs. time graphs? (article) | Khan Academy

relationship between distance time graph and velocity

The more adequate comparison can be drawn between trajectory and velocity, since velocity is the rate of change of trajectory in relation to change in time. Example. Calculate the speed of the object represented by the green line in the graph, from 0 to 4 s. change in distance = (8 - 0) = 8 m. change in time = (4 - 0). Distance -Time Graphs= ''''Distance'''' is the total length travelled by an object. we are asked to determine the connection between speed, position 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?

Motion Graphs - Distance Time Graph And Velocity Time Graph

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.

relationship between distance time graph and velocity

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.

relationship between distance time graph and velocity

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.

BBC Bitesize - GCSE Combined Science - Describing motion - AQA - Revision 3

Maybe right over here, we have the velocity of one meter per second. So if I say one meter per second times the second, that'll give me a little bit of distance. And then the next one I have a little bit more of distance, calculated the same way. I could keep drawing these rectangles here, but then you're like, wait, those rectangles are missing, because I wasn't for the whole second, I wasn't only going one meter per second. So I actually, I should maybe split up the rectangles.

I could split up the rectangles even more. So maybe I go every half second. So on this half-second I was going at this velocity. And I go that velocity for a half-second. Velocity times the time would give me the displacement.

Why distance is area under velocity-time line

And I do it for the next half second. Same exact idea here. Gives me the displacement. So on and so forth. But I think what you see as you're getting-- is the more accurate-- the smaller the rectangles, you try to make here, the closer you're going to get to the area under this curve.

And just like the situation here. This area under the curve is going to be the distance traveled. And lucky for us, this is just going to be a triangle, and we know how to figure out the area for triangle. So the area of a triangle is equal to one half times base times height. Which hopefully makes sense to you, because if you just multiply base times height, you get the area for the entire rectangle, and the triangle is exactly half of that.

These are the lines with arrows on diagram 1.

relationship between distance time graph and velocity

The two values you see are the time and distance where the fast car should overtake the slower car. Mark the predicting passing point on your course. Mark off the calculated point where the faster car should overtake the slower car. Have your assistant release the slower car at the head start mark while you simultaneously release your faster car at the starting line. Start the timer a third person might be nice for this. Watch carefully to see where the fast car overtakes the slow car.

Compare your predicted time and distance that the fast car overtook the slower car with the actual values. Results Your results are likely to be pretty close to what your graph predicts, but they will likely vary depending on the velocities of your cars and whether or not they travel at a consistent velocity.

Conduct more trials if you wish. Uniform velocity is a linear function, making them easy and fun to predict. Although the slower car had a head start in distance, the faster car covered more distance in less time, so it caught up. This is where the lines crossed. A non-graphical way of looking at this is using the following equation: The total distance each car travels to intersect is the same.

Then, you can tell your parents how soon you will arrive at your destination. Disclaimer and Safety Precautions Education. In addition, your access to Education. Warning is hereby given that not all Project Ideas are appropriate for all individuals or in all circumstances. Implementation of any Science Project Idea should be undertaken only in appropriate settings and with appropriate parental or other supervision. Reading and following the safety precautions of all materials used in a project is the sole responsibility of each individual.

For further information, consult your state's handbook of Science Safety. Related learning resources Science project Relationship Between the Distance and Time of a Falling Object In this science fair project on the relationship between distance and time, kids explore the behavior of gravitational acceleration through direct observation.