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# examples of uniform acceleration

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:the concept is from physics, reveal the truth and misconception related to it

Answers:The movement may be sustaining a constant speed, but the body receives a constant acceleration: the centripetal force. If this force is of constant amplitude, it however changes constantly in direction!

Question:hi folks! need sample problems with sol'n about uniformly accelerated motion with 2 object as given. tnx

Answers:consult a physics book.. they have a lot of problems there. =D

Question:Hello, I am a bit confused as to what Uniformly Accelerated Motion Is: Here are a few questions: 1. Is uniformly accelerated motion and uniform accelerated motion the same? 2.Here is my explanation: Uniformly Accelerated motion is when the acceleration stays as a constant (doesn't it get faster and faster though?) and is based on the magnitude of force that pulls the cart (gravity?) 3. Does uniform accelerated motion have do with naturally accelerated motion? 4.Did galileo contribute to this notion? 5. What is the difference with acceleration and speed? For an example a ball rolling down a ramp is uniform accelerated motion. Also, do I graph it with time and velocity as x and y ? Lastly, any good websites on this topic? If you just know a good website explaining this thoroughly, then please feel free to just post that. It would be as helpful as answering the questions Thanks~

Answers:1) yes, just know it as "constant acceleration" or acceleration is constant 2) OK as long as U recognize the DIFFERENCE between velocity and acceleration. These are not the same, and usually one speaks about velocity as being or not being "faster and faster" so I'm just a bit in doubt here. 3) yes, in the sense that "g" the CONSTANT acceleration of gravity = 9.81 m/s in the SI system is acting on us (on the earth) at all times. 4) yes 5)acceleration represents CHANGE in velocity or speed NOT these variables themselves. U can graph IT anyway U like, but usually time (the independent variable) is on the x-axis when plotting motion graphs. just google it - many good sites, not able to search for U

Question:

Answers:When acceleration is 0, velocity will not change and the movement will be through a straight line. Don't forget that accelerations and velocities are vectors. So, while the speed is the same in uniform circular motion (speed is the module of the velocity, that is, the length of the velocity vector), velocity changes direction. And for that effect, there need be an acceleration towards the center of the circle. That's the centripetal force. Example: the Moon around the Earth. The centripetal force of the circular movement of the Moon is known as gravity. (Actualy, that is not exactly circular, but that is not what you asked for)