# 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. • 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 / s2. This means that the object is moving at 5m / s2 accelerated. "A" does not change during the movement, otherwise the acceleration would no longer be uniform.

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### 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 t2 + vO · T + s0
• "s" is the distance in meters [m]
• "a" is the acceleration in meters per second square [m / s2]
• "t" is the time in seconds [s]
• "s0"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 t2

Formula uniformly accelerated movement (speed-time law):

• v = a t + v0
• "v" is the speed in meters per second [m / s]
• "a" is the acceleration in meters per second square [m / s2 ]
• "t" is the time in seconds [s]
• "v0"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 / s2]
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### 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 / s2 ]

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 / s2 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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