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# Difference Between Acceleration and Velocity

Acceleration vs Velocity

Acceleration and velocity are two basic concepts discussed under motion of bodies in physics. In this article, we are going to discuss what acceleration and velocity are, their definitions, similarities and finally the differences between acceleration and velocity.

Velocity

Velocity is defined as the rate of change of displacement between an object and a fixed point. Mathematically speaking velocity equals dx/dt (read as d, dt x) according to the theories of calculus. It is also denoted in ẋ. Velocity also takes the form of angular velocity; in that case velocity is equal to the rate change of angle. Both linear velocity and angular velocity are vectors. Linear velocity has the direction of instantaneous movement, whilst the angular velocity has the direction that is decided by the corkscrew method. Velocity is a relativistic variant, which means the laws of relativity must be applied for velocities compatible with the speed of light. Relative velocity is the velocity of an object relative to another object. In the vector form, this is written as V̰A rel B = V̰A – V̰B. V̰rel is the velocity of object “a” relative to object “b”. Usually a velocity triangle or a velocity parallelogram is used to calculate relative velocity between two objects. Velocity triangle theory states that if VA rel Earth and VEarth rel B are indicated in two sides of a triangle proportional to the magnitude and direction, the third line indicates the direction and magnitude of the relative velocity.

Acceleration

Acceleration is defined as the rate of change of velocity of a body. It is important to notice that acceleration always requires net force acting on the object. This is described in Newton’s second law of motion. The second law states that the net force F on a body is equal to the rate of change of linear momentum of the body. Since the linear momentum is given by the product of mass and velocity of the body and the mass does not change on a non-relativistic scale, the force is equal to the mass times the rate of change of velocity, which is the acceleration. There can be several causes to this force. Electromagnetic force, gravitational force and mechanical force are to name a few. The acceleration due to a mass nearby is known as the gravitational acceleration. It must be noticed that if an object is not subjected to a net force, the object will not change the velocity of itself, whether it was moving or stationary. Note that the movement of the object does not require a force, but the acceleration always does require a force.

 What is the difference between acceleration and velocity? • Acceleration requires net force acting on the object, but velocity does not require such a force. • Every object accelerating has a velocity, but every object having a velocity does not necessarily have to have acceleration. • Acceleration requires a change in the magnitude or the direction of the velocity.

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