# Change in direction and acceleration

• quantizedzeus
In summary: In brief, the acceleration is just the rate of change of velocity. You can find the magnitude of the acceleration by dividing the change in velocity by the change in time.
quantizedzeus
Why and how does Change in direction of a moving body accelerate it?

quantizedzeus said:
Why and how does Change in direction of a moving body accelerate it?
What's the definition of acceleration?

Displacement, velocity and acceleration are vector quantities. A vector quantity not only consists of magnitude (a real number/scalar) but it also consists of direction.

Recall that the definition of acceleration is time rate of change of velocity vector. We care both the magnitude and direction.

You may have a look on the topic of uniform circular motion.

quantizedzeus said:
Why and how does Change in direction of a moving body accelerate it?

It may be mentioned that while the velocity also determines the direction of body , acceleration does not determine the direction of body . Acceleration is a vector quantity because it can be negative . This is because a body can accelerate or retard . Positive and negative sign in acceleration just tell that whether speed is increasing (velocity for particular) or decreasing . For eg. -5m/s2 tell that a body retards by 5m/s velocity .
Change in direction does not bring acceleration . Change in direction means variable velocity and variable velocity means change in velocity per unit time .
Here variable velocity is bringing acceleration . Change in direction is cause of variable velocity.

http://en.wikipedia.org/wiki/Uniform_circular_motion"

Orhttp://www.physicsclassroom.com/mmedia/circmot/ucm.cfm"

Also see scalar and vector quantities.

Vector quantity : Direction + Magnitude and; +ve and -ve. Eg. Displacement , acceleration , velocity etc .

Scalar quantity :Only Magnitude ;and only +ve . Eg. Distance , speed , mass etc .

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Sankalpmittal is not using the term 'acceleration' as physicists use it.

Acceleration is defined as rate of change of velocity. When a body changes its direction it changes its velocity, so it has an acceleration This is not just playing with words: we can even calculate the magnitude of a body's acceleration when it goes in a circle at constant speed.

Strictly, acceleration cannot be positive or negative. It is a vector quantity and has magnitude and direction. Informally, we may talk of accelerations being positive or negative, but we're really talking about the component of acceleration in a chosen direction. The same remark applies to velocities and displacements, indeed to all vectors.

Quantizedzeus... To go a step further, do you know how to subtract vectors? It's the essential skill needed in order to find the acceleration when a body changes direction. You consider a time interval $\delta$t. You find the change in velocity $\delta$v during $\delta$t thus:
$\delta$v = vfinal - vinitial.
The subtraction is, of course, a vector subtraction.
You then divide $\delta$v by $\delta$t to get the mean acceleration during $\delta$t. Finally you find the limit to which this converges as $\delta$t approaches zero, to get the instantaneous acceleration.

The simplest example, and by far the most important case, is a body moving in a circle at constant speed. It is dealt with in almost any standard mechanics text.

## 1. What is the difference between direction and acceleration?

Direction refers to the path that an object is moving in, while acceleration refers to the rate at which an object's velocity is changing. Essentially, direction is the orientation of an object's motion, while acceleration is how quickly that motion is changing.

## 2. How does a change in direction affect an object's acceleration?

When an object changes direction, it means that its velocity is changing, and therefore its acceleration is also changing. The object's acceleration will be in the same direction as its change in direction, meaning that it will be accelerating towards the new direction it is moving in.

## 3. Can an object have a change in direction without a change in acceleration?

No, an object cannot have a change in direction without a change in acceleration. This is because changing direction means that the object's velocity is changing, and any change in velocity results in a change in acceleration.

## 4. How does a change in acceleration affect an object's motion?

A change in acceleration affects an object's motion by either speeding it up, slowing it down, or causing it to change direction. This is because acceleration is directly related to an object's velocity, and any change in velocity will affect the object's motion.

## 5. What factors can cause a change in direction and acceleration?

A change in direction and acceleration can be caused by a variety of factors, including the application of a force, the presence of friction, and the object's mass. For example, if a force is applied to an object in a certain direction, it will change the object's direction and acceleration. Similarly, friction can also cause a change in direction and acceleration by acting in the opposite direction of an object's motion. Additionally, an object's mass can affect its acceleration, as a heavier object requires more force to change its direction and acceleration compared to a lighter object.

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