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From Wikipedia

Acceleration

In physics, acceleration is the rate of change of velocity over time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. Acceleration has the dimensionsL T−2. In SI units, acceleration is measured in meters per second per second (m/s2).

Proper acceleration, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an accelerometer.

In common speech, the term acceleration is used for an increase in speed (the magnitude of velocity); a decrease in speed is called deceleration. In physics, a change in the direction of velocity also is an acceleration: for rotary motion, the change in direction of velocity results in centripetal (toward the center) acceleration; where as the rate of change of speed is a tangential acceleration.

In classical mechanics, for a body with constant mass, the acceleration of the body is proportional to the net force acting on it (Newton's second law):

\mathbf{F} = m\mathbf{a} \quad \to \quad \mathbf{a} = \mathbf{F}/m

where F is the resultant force acting on the body, m is the mass of the body, and a is its acceleration.

Average and instantaneous acceleration

Average acceleration is the change in velocity (Δ'v) divided by the change in time (Δt). Instantaneous acceleration is the acceleration at a specific point in time which is for a very short interval of time as Δt approaches zero.

The velocity of a particle moving on a curved path as a function of time can be written as:

\mathbf{v} (t) =v(t) \frac {\mathbf{v}(t)}{v(t)} = v(t) \mathbf{u}_\mathrm{t}(t) ,

with v(t) equal to the speed of travel along the path, and

\mathbf{u}_\mathrm{t} = \frac {\mathbf{v}(t)}{v(t)} \ ,

a unit vector tangent to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed v(t) and the changing direction of ut, the acceleration of a particle moving on a curved path on a planar surface can be written using thechain rule of differentiation and the derivative of the product of two functions of time as:

\begin{alignat}{3}

\mathbf{a} & = \frac{d \mathbf{v}}{dt} \\ & = \frac{\mathrm{d}v }{\mathrm{d}t} \mathbf{u}_\mathrm{t} +v(t)\frac{d \mathbf{u}_\mathrm{t}}{dt} \\ & = \frac{\mathrm{d}v }{\mathrm{d}t} \mathbf{u}_\mathrm{t}+ \frac{v^2}{R}\mathbf{u}_\mathrm{n}\ , \\ \end{alignat}

where un is the unit (inward) normal vector to the particle's trajectory, and R is its instantaneous radius of curvature based upon the osculating circle at time t. These components are called the tangential accelerationand the radial acceleration or centripetal acceleration (see alsocircular motion and centripetal force).

Extension of this approach to three-dimensional space curves that cannot be contained on a planar surface leads to the Frenet-Serret formulas.

Special cases

Uniform acceleration

Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an equal amount in every equal time period.

A frequently cited example of uniform acceleration is that of an object in free fall in a uniform gravitational field. The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g (also called acceleration due to gravity). By Newton's Second Law the force, F, acting on a body is given by:

\mathbf {F} = m \mathbf {g}

Due to the simple algebraic properties of constant acceleration in the one-dimensional case (that is, the case of acceleration aligned with the initial velocity), there are simple formulae that relate the following quantities: displacement, initial velocity, final velocity, acceleration, and time:

\mathbf {v}= \mathbf {u} + \mathbf {a} t
\mathbf {s}= \mathbf {u} t+ \over {2}} \mathbf {a}t^2 = \over {2}}

where

\mathbf{s} = displacement
\mathbf{u} = initial velocity
\mathbf{v} = final velocity
\mathbf{a} = uniform acceleration
t = time.

In the case of uniform acceleration of an object that is initially moving in a direction not aligned with the acceleration, the motion can be resolved into two orthogonal parts, one of constant velocity and the other according to the above equations. As Galileo showed, the net result is parabolic motion, as in the trajectory of a cannonball, neglecting air resistance.

Circular motion

An example of a body experiencing acceleration of a uniform magnitude but changing direction is uniform <


From Encyclopedia

acceleration

acceleration change in the velocity of a body with respect to time. Since velocity is a vector quantity, involving both magnitude and direction, acceleration is also a vector. In order to produce an acceleration, a force must be applied to the body. The magnitude of the force F must be directly proportional to both the mass of the body m and the desired acceleration a, according to Newton's second law of motion, F = ma. The exact nature of the acceleration produced depends on the relative directions of the original velocity and the force. A force acting in the same direction as the velocity changes only the speed of the body. An appropriate force acting always at right angles to the velocity changes the direction of the velocity but not the speed. An example of such an accelerating force is the gravitational force exerted by a planet on a satellite moving in a circular orbit. A force may also act in the opposite direction from the original velocity. In this case the speed of the body is decreased. Such an acceleration is often referred to as a deceleration. If the acceleration is constant, as for a body falling near the earth, the following formulas may be used to compute the acceleration a of a body from knowledge of the elapsed time t, the distance s through which the body moves in that time, the initial velocity vi , and the final velocity vf :


From Yahoo Answers

Question:What is an example of positive acceleration and what is an example of negative acceleration? (and it can't be a machine.)

Answers:Acceleration is positive when a body is speeding up i.e when the velocity of the body increases with time. Acceleration is negative when a body is slowing down(stopping) i.e when velocity is decreasing with respect to time.

Question:"real life".

Answers:ZERO acceleration would be when you are traveling at a constant speed. POSITIVE acceleration would be when you are increasing speed from one moment to the next. NEGATIVE accleration would be when you are slowing down from one moment to the next.

Question:Can someone please give me an example of an object that has positive or negative acceleration?

Answers:The names "positive" and "negative" depend on you choice of frame of reference. For example, if we're talking about a rocket, we would likely define "positive" acceleration to be the direction [up]. With this choice of coordinates, "negative" acceleration would be in the direction [down]. We are free to choose our coordinate system, so we usually choose one that makes our lives easiest! Remember that acceleration is a vector quantity, meaning that the direction is as important as the magnitude. A rocket with a velocity of -200m/s isn't moving any slower than one going at +200m/s, but it is moving in the opposite direction.

Question:I don't understand when it means negative direction.. is it that soem directions are just considered negative (south and west) OR does it mean that some sort of force is pushing on you not letting you go the direction you want creating that negative acceleration... hopefully you get what i mean! thanks could you also please give a real life example of negative and positive acceleration! thanks

Answers:there is no such thing as negative direction... negative acceleration is deceleration or even negative energy (kinetic being returned)... direction is absolute.

From Youtube

How to Solve a Negative Acceleration Equation :This video walks you through how to solve for negative acceleration when your object starts at a specific velocity and comes to rest in a certain amount of time.

position vs time graph with negative acceleration :Position vs. time graph with negative acceleration is explained by James Dann for CK12.org CC by SA