# Which equations represent the relationship between displacement velocity and time

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

How to analyze graphs that relate velocity and time to acceleration and displacement. The slope of a velocity graph will be given by the following formula: . The area under a velocity graph represents the displacement of the object. To see. These equations of motion are valid only when acceleration is constant and The relation between velocity and time is a simple one during uniformly accelerated, straight-line motion. What velocity is represented by the symbol v? The displacement of a moving object is directly proportional to both velocity and time. Displacement is an integral of velocity over time. First order differential equation is a mathematical relation that relates independent variable, unknown where C1 and C2 are arbitrary constants represents general solution of equation .

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. 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.

## Equations of Motion

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. 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.

### Motion in two dimensions

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. This has nothing to do with the weight of the feather compared to the brick.

It's simply air resistance; if we took away all the air and dropped the feather and brick, they would hit the ground at exactly the same time. So, remember that we're often analyzing ideal cases, especially this early in the semester.

In reality, things might be a little different because of factors we're neglecting at the moment. An example Probably the simplest way to see how to apply these constant acceleration equations is to work through a sample problem.

### Equations of Motion – The Physics Hypertextbook

Let's say you're on top of a cliff, which drops vertically m to a flat valley below. You throw a ball off the cliff, launching it at 8. It's a good idea to be as systematic as possible when it comes to analyzing the situation.

Here's an example of how to organize the information you're given. First, draw a diagram.

Then set up a table to keep track of everything you know. It's important to pick an origin, and to choose a coordinate system showing positive directions.

You don't have to choose the origin or the positive directions this way. Now that everything's neatly organized, think about what can be used to calculate what.

You know plenty of y-information, so we can use that to find the time it takes to reach the ground.

- What are position vs. time graphs?
- What are velocity vs. time graphs?
- What are the kinematic formulas?

One way to do this definitely not the only way is to do it in two steps, first calculating the final velocity using the equation: Taking the square root gives: Remember that the square root can be positive or negative.

In this case it's negative, because the y-component of the velocity will be directed down when the ball hits the ground. Now we can use another equation to solve for time: Rounding off, the ball was in the air for 5.

We can use this time for part bto get the distance traveled in the x-direction during the course of its flight.

## Distance, Velocity and Time: Equations and Relationship

The best equation to use is: So, from the base of the cliff to the point of impact is A point about symmetry At some point in its flight, the ball in the example above returned to the level of the top of the cliff you threw it from the top of the cliff, it went up, and on its way down it passed through a point the same height off the ground as the top of the cliff.

What was the ball's velocity when it passed this height? Its speed will be the same as the initial speed, 8.