Relative Velocity

Relative velocity is the velocity of one body with respect to another body. Suppose two trains A and B are moving parallel to one another with the same velocity and in the same direction. For a passenger in A, B appears to be stationary and vice versa. Thus, the relative velocity of A with respect to B is zero. Also the relative velocity of B with respect to A is zero. If A and B are moving in opposite directions. velocity of A with respect to B is twice the velocity of either. Also the relative velocity of B with respect to A is double. When two trains cross each other on parallel rails in opposite directions, the velocity of one with respect to the other appears to be higher than its own velocity.

Acceleration

The time rate of change of velocity is called acceleration.

Thus acceleration =begin mathsize 20px style a with rightwards arrow on top space equals fraction numerator begin display style stack d v with rightwards arrow on top end style over denominator d t end fraction end style

It is a vector quantity. Its unit is m/s2

(a) Uniform Acceleration: If the velocity of a body increases by equal amounts in equal intervals of time, however small, it is said to move with uniform acceleration. (b) Variable Acceleration: If the velocity of a body increases by unequal amounts in equal intervals of time, however small, it is said to have variable acceleration. The acceleration will be variable if either the magnitude or direction of velocity changes unequally.

Acceleration Due to Gravity

The acceleration with which a freely falling body moves towards the earth is called acceleration due to graviry. If a feather and an iron piece are released from the same height in vacuum, both will reach the ground simultaneously. If they are released in atmosphere, the feather takes a longer time due to air resistance. The force of gravity differs at various locations. It is stronger, for example, at the poles than at the equator. 

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