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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&nbsp;Tâˆ’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):

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 (Î”'v) divided by the change in time (Î”t). Instantaneous acceleration is the acceleration at a specific point in time which is for a very short interval of time as Î”t 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 <

Question:A train started from rest and moved with constant acceleration, At one time it was travelling at 30m/s and 160metres further on it was travelling at 50m/s, how do I find: 1. Acceleration 2.time required to travel the 160m mentioned

Answers:2. time required to travel the 160 m x = .5(vi + vf) * t x = 160 m vi = 30 m/s vf = 50 m/s t = ? 160 = .5(30 + 50) * t 160 = 40 * t t = 160 / 40 = 4 s 1. acceleration over the 160 m vf = vi + a * t 50 = 30 + a * 4 a = (50 - 30) / 4 = 5 m/s/s

Question:I'm trying to simulate a car accelerating but my results are way off. I'm calculating the accelerating force as (power in watts) / ( (velocity in m/s) * (mass in kg) ) is that right? Si units please.

Question:another question,..lol's......anybody can help me for this question?this is my assignment in physics.

Answers:Instantaneous acceleration is acceleration (change of velocity/time) at any given time. In layman's terms, it is the acceleration of a certain body (or particle) at any particular given or chosen instant. Hope this helps.

Question:I am confused! I know instantaneous acceleration is tangent to acceleration graph. But then does that mean instantaneous velocity equal to acceleration since acceleration is tangent of velocity?

Answers:Instantaneous acceleration is the tangent of the **velocity** graph, not the tangent of the acceleration graph. That's probably why you're confused. If you have a graph of acceleration versus time, and you want to know the instantaneous acceleration at any particular time, just read the graph at that time - you don't need to measure the tangent or calculate the slope. You only need to use the tangent or slope if you need to figure out the acceleration from the graph of velocity versus time.

AP Physics B: Instantaneous Acceleration :A free lecture from our AP Physics B series at www.educator.com Other subjects include Algebra, Geometry, Pre-Calculus, Pre-Algebra, Trigonometry, Calculus, Biology, Chemistry, Statistics, and Computer Science. -All lectures are broken down by individual topics -No more wasted time -Just search and jump directly to the answer

Instantaneous Rates of Change: Algebraic Model :Introduction to the algebraic model for calculating instantaneous rates of change. Introduction to the limit concept.