# Acceleration

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Acceleration is the rate of change of an object's velocity. More precisely, it is defined as the derivative of velocity over time, and is a vector. For an object to undergo an acceleration, a force needs to be exerted on the object. An example is a falling object on Earth, which is subject to a gravitational force. The resulting acceleration g is independent of the mass of the object, and is approximately 9.81 meters per second squared near the Earth's surface.

According to Newton's Second Law of Motion, calculation of acceleration is done with the formula , where F is the force, measured in Newtons, m is the mass, measured in kilograms and a is the acceleration, measured in meters per second squared. Using the formula we can see that . This formula is only correct when the mass is constant.

In the case of straight trajectory, if an object's acceleration and velocity have the same direction, the object is gaining speed. If the acceleration and velocity have opposite directions, the object is losing speed. If the acceleration is zero, then the object is either at rest or travelling in a straight line at constant speed. This is Newton's first law that the velocity of an object is constant if the net force acting on it is zero.

In case of a curvilinear trajectory, there is an acceleration, even if the speed of the object is constant. This is because the direction of the object's velocity changes if the path is curved. And whenever there is a change in velocity, there is an acceleration, since acceleration is the change in velocity with respect to time. An example of this is circular motion, where the speed of a particle is constant, but it is accelerating towards the centre of its circular trajectory.