Question

express average velocity,instantaneous velocity,acceleration and instantaneous acceleration in terms of vectors(actually,resolution of vectors) with examples.

Answer 1

Average velocity:
It is a vector which is obtained by the ratio of displacement vector and time taken.
Ex: When the displacement of a car is 100 m towards north in 10 s, then its average velocity vector is 10 m/s in north direction.

Instantaneous velocity:
It is a vector which represents the velocity of a body at the given instant.
Ex: When the velocity of a car is 10 m/s towards north during 10th second of its motion, then the instantaneous velocity of the car at 10th second is 10 m/s towards north.

Acceleration;
It is a vector which is obtained by the ratio of change in velocity vectors in the given time interval and the time taken.
Ex: When the velocity of a car is 10 m/s north at 1st second and 30 m/s north at 2nd second, then its acceleration vector is 20 m/s² north.

Instantaneous acceleration:
It is a vector which represents the acceleration of a body at the given instant.
Ex: When the acceleration of a car is 10 m/s² towards north during 10th second of its motion, then the instantaneous acceleration vector of the car at 10th second is 10 m/s² towards north.