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 / 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.

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