Acceleration

In physics, acceleration is the rate of change of velocity of an object with respect to time. An object's acceleration is the net result of all forces acting on the object, as described by Newton's Second Law. The SI unit for acceleration is metre per second squared (m⋅s−2). Accelerations are vector quantities (they have magnitude and direction) and add according to the parallelogram law. The vector of the net force acting on a body has the same direction as the vector of the body's acceleration, and its magnitude is proportional to the magnitude of the acceleration, with the object's mass (a scalar quantity) as proportionality constant. For example, when a car starts from a standstill (zero velocity, in an inertial frame of reference) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the car turns, an acceleration occurs toward the new direction. The forward acceleration of the car is called a linear (or tangential) acceleration, the reaction to which passengers in the car experience as a force pushing them back into their seats. When changing direction, this is called radial (as orthogonal to tangential) acceleration, the reaction to which passengers experience as a sideways force. If the speed of the car decreases, this is an acceleration in the opposite direction of the velocity of the vehicle, sometimes called deceleration or Retrograde burning in spacecraft. Passengers experience the reaction to deceleration as a force pushing them forwards. Both acceleration and deceleration are treated the same, they are both changes in velocity. Each of these accelerations (tangential, radial, deceleration) is felt by passengers until their velocity (speed and direction) matches that of the uniformly moving car. An object's average acceleration over a period of time is its change in velocity ( Δ v ) {displaystyle (Delta mathbf {v} )} divided by the duration of the period ( Δ t ) {displaystyle (Delta t)} . Mathematically, Instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time. In the terms of calculus, instantaneous acceleration is the derivative of the velocity vector with respect to time: (Here and elsewhere, if motion is in a straight line, vector quantities can be substituted by scalars in the equations.) It can be seen that the integral of the acceleration function a(t) is the velocity function v(t); that is, the area under the curve of an acceleration vs. time (a vs. t) graph corresponds to velocity. As acceleration is defined as the derivative of velocity, v, with respect to time t and velocity is defined as the derivative of position, x, with respect to time, acceleration can be thought of as the second derivative of x with respect to t: Acceleration has the dimensions of velocity (L/T) divided by time, i.e. L T−2. The SI unit of acceleration is the metre per second squared (m s−2); or 'metre per second per second', as the velocity in metres per second changes by the acceleration value, every second.