Velocity and Acceleration

Velocity

Velocity describes how fast an object is moving. The difference between velocity and speed is that velocity is a vector. For example, if an object first moves 5 meters forward in 1 second and then moves 4 meters backward in 2 second. The speed for the object should be 5ms^-1 and 2ms^-1 while the velocity for the object is 5ms^-1 and -2ms^-1 (there is an negative sign).

Moreover, the average speed for the whole journey is 3ms^-1 while the average velocity is 0.33ms^-1.

So, how to define average velocity? The average velocity is defined as displacement divided by time taken.

Instantaneous velocity represent the rate of change of displacement at a particular time.

We can denote that with the equation

Acceleration

Acceleration describes how the velocity is changing. The relationship between acceleration and velocity is like the relationship between velocity and displacement.

The average acceleration of an object is defined as

For example, if a car increases its velocity to 30ms^-1 from rest in 15 seconds, then the acceleration is 2ms^-2

If the time taken is very small, the average acceleration represents the instantaneous acceleration (acceleration at a particular time) which is defined as the rate of change of velocity.

a =

Acceleration is a vector quantity. For uniform velocity, a = 0. If a is a non-zero constant, the object is said to be uniformly accelerated