# Equations representing the relationship between distance time and velocity

### Sci Lab: Describing Motion

So his average speed will be non zero. The relation between distance, time and speed is,. Distance = average speed * time. Average Velocity v = displacement. These equations of motion are valid only when acceleration is constant and motion is The relation between velocity and time is a simple one during uniformly accelerated, straight-line motion. What velocity is represented by the symbol v? A car accelerating for two seconds would cover four times the distance of a car. Recognize the RELATIONSHIPS between numbers, equations, and graphs. Understand the RELATIONSHIPS between distance and time for constant and Understand the meaning of the slope and area of a graph of velocity vs. time . The numbers in table 4 represent the distance traveled in equal time intervals by a.

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.

## Describing motion - AQA

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.

Are any of these the final velocity? Someone could extract the meteorite from its hole in the ground and drive away with it. Probably not, but it depends. There's no rule for this kind of thing.

You have to parse the text of a problem for physical quantities and then assign meaning to mathematical symbols. The last part of this equation at is the change in the velocity from the initial value. Recall that a is the rate of change of velocity and that t is the time after some initial event.

Rate times time is change. Move longer as in longer time. Acceleration compounds this simple situation since velocity is now also directly proportional to time. Try saying this in words and it sounds ridiculous. Would that it were so simple. Another way to interpret Newton's 2nd Law is to say that the net sum total force on an object is what causes its acceleration.

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

Hence, there may be any number of forces acting on an object, but it is the resultant of all of them that actually causes any acceleration. Remember, however, that these are force vectors, not just numbers. We must add them just as we would add vectors. A simple if-then statement that holds true due to Newton's 2nd Law.

If the mass is not accelerated meaning: This is not to say that there is no force acting on it, just that the sum total of all the forces acting on it is equal to zero -- all the forces "cancel out". Since force is a vector, I can simply focus on its components when I wish.

**Equation for Position-Velocity Relation**

So, if I have a series of forces acting on a mass, the sum of their x-components must be equal to the x-component of the net force on the mass. And, by Newton's 2nd Law, this must be equal to the mass times the x-component of the acceleration since mass has no direction, and acceleration is also a vector. Similarly as above, if I have a series of forces acting on a mass, the sum of their y-components must be equal to the y-component of the net force on the mass.

## Distance, Velocity and Time: Equations and Relationship

And, by Newton's 2nd Law, this must be equal to the mass times the y-component of the acceleration since mass has no direction, and acceleration is also a vector. If we calculate or just know the x- and y-components of the net force acting on an object, it is a snap to find the total net force. As with any vector, it is merely the sum of its components added together like a right triangle, of course.

This equation becomes ridiculously easy to use if either one of the components is zero. The definition of momentum is simply mass times velocity. Take note that an object can have different velocities measured from different reference frames. Newton's 2nd Law re-written as an expression of momentum change. This is actually how Newton first thought of his law. It allows us to think of momentum change as "impulse" force over some timeand apply the law in a much simpler fashion.

In a closed, isolated system, the total momentum of all the objects does not change. Since "closed" means nothing coming in or going out, we can imagine all our applications talking about a fixed set of objects.

Since "isolated" means no interactions with anything outside the system, we must imagine all our applications involve nothing but those objects and forces that we consider. In two dimensions, the law still holds -- we just pay attention to the components of the total momentum.

Here, a' refers to object a after the collision. This equation shows the relationship between arclength sradius rand angle theta - measured in radians. It is useful for finding the distance around any circular path or portion thereof at a given radial distance. This equation shows the relationship between the period of a pendulum and its length. It was first discovered by Galileo that the arc of a pendulums swing and the mass at the end of a pendulum do not factor noticeably into the amount of time each swing takes.

Only the length of the pendulum matters. The tangential velocity of an object in uniform unchanging circular motion is how fast it is moving tangent to the circle. Literally the distance around the circle divided by the period of rotation time for one full rotation.

The centripetal acceleration of an object in uniform circular motion is how much its velocity because of direction, not speed changes toward the center of the circle in order for it to continue moving in a circle. The force that is required to keep an object moving in a circular path is the centripetal force acting on the object. This force, directed towards the center of the circle, is really just a derivative of Newton's 2nd Law using centripetal acceleration.

The work done on an object is found by multiplying force and distance, but there is a catch. The force and distance must be parallel to each other.

Only the component of the force in the same direction as the distance traveled does any work. Hence, if a force applied is perpendicular to the distance traveled, no work is done. The equation becomes force times distance times the cosine of the angle between them. Work is measured in units of newtons times meters, or joules J. Power is a physical quantity equal to the rate at which work is done. The more time it takes to do the same work, the smaller the power generated, and vice-versa.