# How are speed mass and acceleration connected?

## Speed acceleration

**This article deals with the calculation of the acceleration and the resulting speed during a movement. We will provide you with the appropriate formulas and then go into the acceleration work. This article belongs to the field of physics or mechanics.**

This article is about smoothly accelerated motion. This has the following properties:

- The speed of the object changes, becomes either faster or slower
- Thus the acceleration - usually designated with "a" - is not equal to zero
- The acceleration is always constant in the case of a uniformly accelerated movement

So again: the acceleration is always the same. Example: a = 5m / s^{2}. This means that the object is moving at 5m / s^{2} accelerated. "A" does not change during the movement, otherwise the acceleration would no longer be uniform.

**Relationship: speed acceleration**

**Relationship: speed acceleration**

There are three laws of uniformly accelerated motion. These laws provide information too **Distance, acceleration, time, initial speed and initial distance**.

**Formula uniformly accelerated movement (distance-time law):**

**s = 0.5 a t**^{2}+ v_{O}· T + s_{0}- "s" is the distance in meters [m]
- "a" is the acceleration in meters per second square [m / s
^{2}] - "t" is the time in seconds [s]
- "s
_{0}"is the starting path [m]

If the movement starts from a standstill and from the starting point, the formula simplifies to: ** s = 0.5 a t ^{2}**

**Formula uniformly accelerated movement (speed-time law):**

**v = a t + v**_{0}- "v" is the speed in meters per second [m / s]
- "a" is the acceleration in meters per second square [m / s
^{2}] - "t" is the time in seconds [s]
- "v
_{0}"is the initial speed in meters per second [m / s]

If the movement begins without a start speed, the formula is simplified to: **v = a t****Formula uniformly accelerated movement (acceleration-time law):**

- a = constant
- "a" is the acceleration in meters per second square [m / s
^{2}]

**Speed and acceleration: examples **

Time to calculate one or the other example of uniformly accelerated movement (including speed).

**Example 1:**

**Example 2:**

**Conversion of units**

Many students have problems converting units. For this reason, we are going to give you a short summary of the most important conversion rules.

- 100cm = 1m = 0.001km
- 1m / s = 3.6km / h

**Acceleration work: what is it?**

The **Acceleration work is a kind of mechanical work**. For this reason, you should now briefly get to know the definition of mechanical work, if you do not yet know it: Mechanical work is performed when a body is moved or deformed by a force. The symbol for the work is the "W". Joule (J) or Newton meter (Nm) is used as the unit. Here 1J = 1Nm.

Now we come to the acceleration work: **If a body is accelerated, acceleration work is done**. An example: A train is standing in the station and is now moving off. To make this possible, the train has to accelerate - in other words, become faster - and thereby perform work in the physical sense. There are several formulas in this context, which we would like to consider in more detail below:

**Formula 1:**

- "W" is the acceleration work in Newton meters [Nm]
- "F.
_{B.}"is the force during acceleration in Newtons [N] - "s" is the distance in meters [m]
- "m" is the mass in kilograms [kg]
- "a" is the acceleration in meters per second square [m / s
^{2}]

**Formula 2:**

- "W" is the work in Newton meters [Nm]
- "m" is the mass in kilograms [kg]
- "v" is the speed in meters per second [m / s]

**annotation**: Formula 2 is also known from the field of kinetic energy. This relationship is obtained by inserting the velocity and acceleration equations of the accelerated motion into the work formula.

**Example:**

A car weighing 2000kg accelerates at 3m / s^{2} over a path of 200 meters. How much acceleration work was done?

Solution: We take the necessary information from the text and insert it into the formula.

**Left:**

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