# Acceleration: Why 2 Formulas & How Does It Relate to Distance?

• LT72884
In summary, acceleration is measured in units of distance per time squared and is related to distance, speed, and time through various formulas.
LT72884
Why are there two formulas for acceleration?

A=Change of velocity/time
A=Force/Mass

Ok, now that that's out of the way, i need some light shed on a subject. If acceleration or gravity perse is 10m/s^2, how does this relate to distance.. Meters is a distance. So if an object falls 2 seconds, that is 20m/s^2 of acceleration. According to my book, how far an object falls is not the same as how fast.. If 9.8 is a constant, can't we treat it like velocity, such as, if i am driving at a velocity of 16.66m/s(60kmh) then in one hour i have gone 60km.

d=1/2(g)(t)^2 i know how to use the formula. haha. but why is acceleration measured in a unit of distance if it has nothing to do with distance.

I know that as soon as i drop a brick from a building, it takes a FULL second to reach that constant BUT as soon as it does reach that, isn't the distance the object falls at any given second after the first, going to be 10m/s? for example, i drop a brick off a dang building, between the third and fourth second, didnt it fall a distance of 10m/s because the constant was established after the first second and meters per second is a distance?

thanx

LT72884 said:
Why are there two formulas for acceleration?

A=Change of velocity/time
A=Force/Mass
The first is the definition of acceleration; the second is Newton's 2nd law.

Ok, now that that's out of the way, i need some light shed on a subject. If acceleration or gravity perse is 10m/s^2, how does this relate to distance..
Given the acceleration, the initial velocity, and the time, you can compute the distance using basic kinematics.
Meters is a distance. So if an object falls 2 seconds, that is 20m/s^2 of acceleration.
No, the acceleration remains 10 m/s^2. After 2 seconds of falling the speed is 20 m/s (not m/s^2).

According to my book, how far an object falls is not the same as how fast.. If 9.8 is a constant, can't we treat it like velocity, such as, if i am driving at a velocity of 16.66m/s(60kmh) then in one hour i have gone 60km.
9.8 m/s^2 is a constant. But it's an acceleration, not a speed.

d=1/2(g)(t)^2 i know how to use the formula. haha. but why is acceleration measured in a unit of distance if it has nothing to do with distance.
Obviously it has something to do with distance--you just gave the formula for it! Acceleration is measured in units of distance over time squared (a speed per unit time).

I know that as soon as i drop a brick from a building, it takes a FULL second to reach that constant BUT as soon as it does reach that, isn't the distance the object falls at any given second after the first, going to be 10m/s? for example, i drop a brick off a dang building, between the third and fourth second, didnt it fall a distance of 10m/s because the constant was established after the first second and meters per second is a distance?
As soon as you drop the brick its acceleration is 10 m/s^2. After 1 second, its speed is 10 m/s. The speed--not the acceleration--takes a full second to reach 10 m/s. The acceleration is immediately 10 m/s^2.

To get the distance fallen between the 3rd and 4th second, use the formula for distance that you quoted.

## 1. What are the two formulas for acceleration?

The two formulas for acceleration are average acceleration (a = Δv/Δt) and instantaneous acceleration (a = dv/dt).

## 2. How are these two formulas related to distance?

These two formulas for acceleration are related to distance through the concept of velocity. Velocity is the rate at which an object changes its position, and acceleration is the rate at which an object changes its velocity. Therefore, acceleration is a measure of how quickly an object's distance changes over time.

## 3. Why are there two different formulas for acceleration?

There are two different formulas for acceleration because average acceleration measures the overall change in velocity over a period of time, while instantaneous acceleration measures the change in velocity at a specific moment in time. Both formulas are useful in different situations, such as when studying the motion of an object over a certain distance or when analyzing the motion of an object at a specific point in time.

## 4. How can acceleration be calculated using these formulas?

To calculate acceleration using these formulas, you need to know the change in velocity (Δv) and the change in time (Δt). For average acceleration, simply divide the change in velocity by the change in time. For instantaneous acceleration, you will need to take the derivative of the velocity function with respect to time.

## 5. What are some real life examples of acceleration and its relationship to distance?

Some real life examples of acceleration and its relationship to distance include a car accelerating from a stop sign, a person jumping off a diving board, and a roller coaster going down a steep drop. In all of these scenarios, the distance traveled by the object is directly related to the acceleration it experiences. The faster the acceleration, the more distance the object will cover in a given amount of time.

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