Speed: The rate at which a moving body describes its path is called as speed or the rate of change of distance with respect to time is termed as speed.
E.g.; If the length of the path followed by a moving body between two points P and Q is 20 km and the time taken to travel this path is 2 hrs, then the speed of the body is 20 km/2 hr = 10 km/hr. The path followed by the body may be curved or a straight line and its shape have no concern with the speed of the body.
Speed is purely a scalar quantity and hence it has magnitude only.
Velocity: The rate of change of displacement with respect to time is called as velocity.
E.g.; If ∆x represents the displacement of the body in time interval ∆t, then the velocity of the body is defined as
v = ∆x/∆t
In the limiting case when ∆t →0, v = Lim∆t→0 ∆x/∆t = dx/dt
Velocity is also expressed by both magnitude and direction just like displacement. Hence velocity is a vector quantity.
Relative velocity: The velocity of a body or with respect to another body is termed as relative velocity.
How to find relative velocities in different cases:
Case 01. When two bodies are moving along a straight line in the same direction (say body A and B), the magnitude of the relative velocity of body A with respect to B is just equal to the difference of the magnitudes of their velocities, i.e. magnitude of the velocity of body A minus magnitude of velocity of body B.
Therefore, vAB = vA vB
Case 02. When two bodies are moving along a straight line in the opposite direction (say body Aand B), the magnitude of the relative velocity of body A with respect to B is just equal to the sum of the magnitudes of their velocities.
Therefore, vAB = vA + vB
Case 03. Motion of a body on a body in the same direction: If a train is moving with velocity v1 and a man is running inside it in the same direction with a velocity v2, then,
Relative velocity of man with respect to earth is = v1 + v2
Case 04. Motion of a body on a body in the opposite direction: If a train is moving with velocity v1 and a man is running inside it in a direction opposite to that of train with a velocity v2, then,
Relative velocity of man with respect to earth is = v1 - v2