# Mathematical relationship between velocity and time

### Velocity - Wikipedia

Speed (velocity) is the rate of change of distance (displacement) with time. If you know a little about mathematics, these statements are meaningful and useful. (The symbol v is used for speed because of the association between speed and. If the initial velocity is u, and the acceleration due to gravity is g, then the velocity v at time t satisfies: v = u - gt. If t = 0 and u = 15 m/s., then. Since we are trying to find a relatioanship between distance, time and velocity. Instead of using distanceto find the velocity, we need to use displacemet.

This is a notion that many people have difficulty with. It is possible to be accelerating and yet not be moving but only for an instant, of course. Some interpret this as motion in reverse, but is this generally the case? Well, this is an abstract example. It's not accompanied by any text.

Graphs contain a lot of information, but without a title or other form of description they have no meaning. What does this graph represent? A mote of dust?

About all we can say is that this object was moving at first, slowed to a stop, reversed direction, stopped again, and then resumed moving in the direction it started with whatever direction that was. Negative slope does not automatically mean driving backward, or walking left, or falling down. The choice of signs is always arbitrary.

About all we can say in general, is that when the slope is negative, the object is traveling in the negative direction. On a displacement-time graph… positive slope implies motion in the positive direction. There is something about a line graph that makes people think they're looking at the path of an object.

Don't think like this. Don't look at these graphs and think of them as a picture of a moving object.

## Speed & Velocity

Using your calculated velocities, you will now are going to determine how long your faster car could delay and still overtake the slower car. Make sure to make your graph large so you have room to expand it if necessary!

On the Y axis, mark the distance in centimeters from zero to centimeters. Remember— centimeters is the same as 1. Plot the velocity of the slower car. Your first point should be at 0,20 cm because you are going to give it a cm head start. Your second point for the slow car is the velocity you measured. The X value should be whatever time it took for the car to reach the end of your test course, your Y value is the distance you had the car travel 1.

Using your ruler and pencil, connect the two points to make a line.

Now, plot the velocity of the faster car. Your first point should be at 0,0 cm because this car will not get a head start.

### How are acceleration, time and velocity related? | Socratic

Your second point for the fast car is the velocity you measured. Using your ruler and pencil connect the two points to make another line. Make this line look different than the first, either by making dashes or making it darker.

Label the lines fast car and slow car. Find where the two lines cross. At this intersection point, trace one line to X axis, and another to the Y axis. These are the lines with arrows on diagram 1. 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.

**Why distance is area under velocity-time line - Physics - Khan Academy**

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.

- Graphs of Motion
- How are acceleration, time and velocity related?
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