# Is acceleration correlated with an instantaneous velocity?

• gomer36
In summary, acceleration is the rate of change of velocity with respect to time. Instantaneous acceleration determines how instantaneous velocity changes in an infinitesmall amount of time, while average acceleration correlates to the velocities of a time interval. To find instantaneous acceleration, we need to know the instantaneous velocity for every t inside the time interval. Similarly for velocity, we need to know the instantaneous location for every t inside an interval. At any instant, the instantaneous velocity can be defined as v(t).

#### gomer36

Is acceleration correlated with an instantaneous velocity? tia

yes, acceleration is the rate of change of velocity respect to time.

gsal said:
yes, acceleration is the rate of change of velocity respect to time.

thank you

Yes, since instantaneous acceleration is dv/dt, so this instantaneous acceleration determines how instantaneous velocity changes in an infinitesmall amount of time. i.e. the instantaneous acceleration determines how the instantaneous velocity changes in the vicinity of that instance.

Only instantaneous acceleration relates to instantaneous velocity. An average acceleration correlates to the two velocities of a time interval. For example if we have the time interval from $$t_1$$ to $$t_2$$ then the average acceleration for this time interval is $$a_{avg}=\frac{v_2-v_1}{t_2-t_1}$$ where v2 and v1 the velocities at time t2 and t1.

But to find the instantaneous acceleration we need to know the instanteneous velocity v(t) for every t inside (t1,t2) and not just only the two velocities v2 and v1 at the edges of the time interval t2 and t1. If we know v(t) then the instantaneous acceleration is $$a(t)=\frac{dv(t)}{dt}$$.

ZealScience said:
instantaneous acceleration determines how instantaneous velocity changes in an infinitesmall amount of time.

So, at any instant, can the instantaneous velocity be defined, or is it changing? ()

Delta² said:
But to find the instantaneous acceleration we need to know the instanteneous velocity v(t) for every t inside (t1,t2) and not just only the two velocities v2 and v1 at the edges of the time interval t2 and t1. If we know v(t) then the instantaneous acceleration is $$\frac{dv(t)}{dt}$$.

Similarly for velocity, we need to know the instantaneous location for every t inside an interval. If you know a location without also knowing what its location is at +Δt and -Δt then you cannot determine its velocity, but if you require a small interval of time to work out how it is moving, then it is no longer 'instantaneous'?!

cmb said:
So, at any instant, can the instantaneous velocity be defined, or is it changing? ()

Can be defined and its value at any instant t is v(t)

## 1. What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude (speed) and direction.

## 2. What is instantaneous velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time. It is the slope of the tangent line to the object's position-time graph at that point.

## 3. How are acceleration and instantaneous velocity related?

Acceleration and instantaneous velocity are related in that acceleration is the change in instantaneous velocity over time. In other words, acceleration is the rate at which an object's velocity is changing at a given moment in time.

## 4. Is there a correlation between acceleration and instantaneous velocity?

Yes, there is a correlation between acceleration and instantaneous velocity. As acceleration increases, the change in instantaneous velocity also increases. This means that if an object is accelerating, its instantaneous velocity is changing at a faster rate.

## 5. How can we calculate acceleration and instantaneous velocity?

Acceleration can be calculated by dividing the change in velocity by the change in time. Instantaneous velocity can be calculated by finding the slope of the tangent line to the object's position-time graph at a specific point. Both can also be calculated using calculus equations, such as derivatives and integrals.