# Displacement vs time relationship of action

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

are used, you usually freeze the action at a particular instant in time, This linear relationship between the force and the displacement is. More precisely, we need to specify its position relative to a convenient reference frame. Earth is often used as a reference frame, and we often describe the. Sometimes you need a picture — a mathematical picture called a graph. The relation between displacement and time is quadratic when the acceleration . This inverse relation between the actions of derivative (slope) and integral (area) is.

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.

### Graphs of Motion – The Physics Hypertextbook

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.

## Representing Free Fall by Graphs

Instead, think of them as the record of an object's velocity. In these graphs, higher means faster not farther. These particular graphs are all horizontal.

The initial velocity of each object is the same as the final velocity is the same as every velocity in between. The velocity of each of these objects is constant during this ten second interval.

### Velocity - Wikipedia

In comparison, when the curve on a velocity-time graph is straight but not horizontal, the velocity is changing. The three curves to the right each have a different slope. Note that the work in this equation is the work done by the net force, rather than the work done by an individual force.

Gravitational potential energy Let's say you're dropping a ball from a certain height, and you'd like to know how fast it's traveling the instant it hits the ground.

You could apply the projectile motion equations, or you could think of the situation in terms of energy actually, one of the projectile motion equations is really an energy equation in disguise. If you drop an object it falls down, picking up speed along the way.

## Graphs of Motion

This means there must be a net force on the object, doing work. This force is the force of gravity, with a magnitude equal to mg, the weight of the object.

The work done by the force of gravity is the force multiplied by the distance, so if the object drops a distance h, gravity does work on the object equal to the force multiplied by the height lost, which is: An object with potential energy has the potential to do work.

In the case of gravitational potential energy, the object has the potential to do work because of where it is, at a certain height above the ground, or at least above something. Spring potential energy Energy can also be stored in a stretched or compressed spring.

An ideal spring is one in which the amount the spring stretches or compresses is proportional to the applied force. This linear relationship between the force and the displacement is known as Hooke's law. For a spring this can be written: The larger k is, the stiffer the spring is and the harder the spring is to stretch. If an object applies a force to a spring, the spring applies an equal and opposite force to the object. This is a restoring force, because when the spring is stretched, the force exerted by by the spring is opposite to the direction it is stretched.

**Displacement Velocity Acceleration Time Graphs - Slope & Area - Physics - Distance, Speed, Position**

This accounts for the oscillating motion of a mass on a spring. If a mass hanging down from a spring is pulled down and let go, the spring exerts an upward force on the mass, moving it back to the equilibrium position, and then beyond. This compresses the spring, so the spring exerts a downward force on the mass, stopping it, and then moving it back to the equilibrium and beyond, at which point the cycle repeats.

This kind of motion is known as simple harmonic motion, which we'll come back to later in the course. The potential energy stored in a spring is given by: In a perfect spring, no energy is lost; the energy is simply transferred back and forth between the kinetic energy of the mass on the spring and the potential energy of the spring gravitational PE might be involved, too. Conservation of energy We'll take all of the different kinds of energy we know about, and even all the other ones we don't, and relate them through one of the fundamental laws of the universe.