Some Definitions

Scalar Quantity: A quantity, in which direction is not important, i.e. only magnitude is important is called scalar quantity. e.g. speed, distance etc.

Vector Quantity: A quantity, in which direction as well as magnitude are important is called a vector quantity. e.g. velocity, displacement etc.

Speed: Distance covered by a body per unit time is called speed.

S = D / T

Where
      S = Speed of the body.
      D = Distance travelled by the body.
      T = Time taken

Displacement: Displacement is the distance between starting and ending point in a given time. The difference between distance and displacement is evident from the following picture:

In this figure, total distance traveled in a given time is d1 + d2, whereas displacement is the distance D between starting and ending point. This makes it very clear that distance is a scalar quantity, whereas displacement is a vector quantity.

Velocity: Displacement obtained by a body per unit time is called velocity.

V = D / T

Where
      V = Velocity
      D = Displacement obtained
      T = Time taken

If time is very small, then we can say that:

V = dD/dT

Displacement is a vector quantity. Hence, velocity is also a vector quantity. In this way, we can say that velocity is to speed what displacement is to distance.

Acceleration Velocity gained by a body per unit time is called acceleration.

A = V /T

Where
       A = Acceleration
       V = Velocity
       T = Time

For elementary time:

A = dV / dT