# Instantaneous velocity and acceleration relationship

### Difference between instantaneous velocity and acceleration | Physics Forums to that constant velocity. During that acceleration, the velocity was not constant. The graph was not a straight line. The definition of instantaneous velocity. Average speed is described as a measure of distance divided by time. Velocity can be constant, or it can change (acceleration). Speed with a direction is velocity . Section - Instantaneous Velocity and Acceleration If we were given the relationship for distance covered as a function of time t, then velocity of the car at .

Average acceleration symbol 'a' is a change in velocity per unit time, or Acceleration is a vector quantity - it has both magnitude and direction. We can accelerate an object by changing its speed over a time interval, such as speeding up or slowing down in your car. We are familiar with the right hand gas pedal on a car - we call it the "accelerator.

We can also change the velocity of an object by changing the direction the object is moving. So in a car, the steering wheel is also a type of "accelerator". The units of acceleration are units of velocity per unit time. Again, we will use positive and negative signs to show the direction of our acceleration.

What we choose as positive left, right, up, down, etc is largely a matter of personal preference, but we will see in some later problem solving examples that sometimes it makes sense to choose our sign conventions in a specific way.

We can make some interesting observations which may conceptually help us understand signs. An example of this is a car with its brakes on. An object may be at rest zero velocity and have positive acceleration such as a car just starting from rest; it is the acceleration on the car that causes a change in velocity. There are other examples that we will discuss in future lessons. Motion with Uniform Acceleration The next thing to consider is a specialized case of acceleration which we will study for quite some time: We sometimes call this uniformly accelerated motion.

Here are the assumptions for our next steps: An object is moving in a straight line The rate of change of velocity is uniform the same.

Our initial position and velocity will be referred to as xo and vo. Find instantaneous acceleration at a specified time on a graph of velocity versus time. The importance of understanding acceleration spans our day-to-day experience, as well as the vast reaches of outer space and the tiny world of subatomic physics.

In everyday conversation, to accelerate means to speed up; applying the brake pedal causes a vehicle to slow down. We are familiar with the acceleration of our car, for example.

## Acceleration

The greater the acceleration, the greater the change in velocity over a given time. Acceleration is widely seen in experimental physics. In linear particle accelerator experiments, for example, subatomic particles are accelerated to very high velocities in collision experiments, which tell us information about the structure of the subatomic world as well as the origin of the universe.

In space, cosmic rays are subatomic particles that have been accelerated to very high energies in supernovas exploding massive stars and active galactic nuclei. It is important to understand the processes that accelerate cosmic rays because these rays contain highly penetrating radiation that can damage electronics flown on spacecraft, for example.

Average Acceleration The formal definition of acceleration is consistent with these notions just described, but is more inclusive. Average Acceleration Average acceleration is the rate at which velocity changes: The bar over the a means average acceleration. This literally means by how many meters per second the velocity changes every second.

Position, Velocity, Acceleration using Derivatives

Recall that velocity is a vector—it has both magnitude and direction—which means that a change in velocity can be a change in magnitude or speedbut it can also be a change in direction. Thus, acceleration occurs when velocity changes in magnitude an increase or decrease in speed or in direction, or both. Since velocity is a vector, it can change in magnitude or in direction, or both. Acceleration is, therefore, a change in speed or direction, or both. Keep in mind that although acceleration is in the direction of the change in velocity, it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. Although this is commonly referred to as deceleration Figure 3. A subway train in Sao Paulo, Brazil, decelerates as it comes into a station.

It is accelerating in a direction opposite to its direction of motion. Yusuke Kawasaki The term deceleration can cause confusion in our analysis because it is not a vector and it does not point to a specific direction with respect to a coordinate system, so we do not use it.

Acceleration is a vector, so we must choose the appropriate sign for it in our chosen coordinate system.

### - Instantaneous Velocity and Acceleration

In the case of the train in Figure 3. If an object in motion has a velocity in the positive direction with respect to a chosen origin and it acquires a constant negative acceleration, the object eventually comes to a rest and reverses direction.

If we wait long enough, the object passes through the origin going in the opposite direction. This is illustrated in Figure 3. An object in motion with a velocity vector toward the east under negative acceleration comes to a rest and reverses direction. It passes the origin going in the opposite direction after a long enough time.

## INSTANTANEOUS VELOCITY

A Racehorse Leaves the Gate A racehorse coming out of the gate accelerates from rest to a velocity of What is its average acceleration? Racehorses accelerating out of the gate.

Jon Sullivan Strategy First we draw a sketch and assign a coordinate system to the problem Figure 3. This is a simple problem, but it always helps to visualize it.

Notice that we assign east as positive and west as negative. Thus, in this case, we have negative velocity. Identify the coordinate system, the given information, and what you want to determine. Solution First, identify the knowns: Second, find the change in velocity.

Since the horse is going from zero to — An acceleration of 8. This is truly an average acceleration, because the ride is not smooth. We see later that an acceleration of this magnitude would require the rider to hang on with a force nearly equal to his weight.