1) Average velocity and instantaneous velocity are generally two different quantities. Can they ever be equal by a specific motion??

2) If average velocity is not equal to zero, for some time interval, change in "T" , does it mean that the instantaneous velocity is never zero during the interval

3) If the velocity of a particles is zero, can it acceleration ever be non - zero and vice versa

4) Can the magnitude of a particles displacement be greater than distance traveled

5) Can the magnitude of a resultant be negative?

reccy:
1) Average velocity and instantaneous velocity are generally two different quantities. Can they ever be equal by a specific motion??

Yes. If the displacement function s(t) is continuous on a closed interval, say [a , b ] and it's differentiable on (a , b ) then there exists at least a time, say c, in (a , b ) such that:

s'(c) = [s(b) - s(a)]/(b - a)

This is called the Mean Value Theorem.

2) If average velocity is not equal to zero, for some time interval, change in "T" , does it mean that the instantaneous velocity is never zero during the interval

The instantaneous velocity can be zero. This is a no brainer na.

3) If the velocity of a particles is zero, can it acceleration ever be non - zero and vice versa

If the velocity of a particle is 0 then the acceleration is always zero. Remember that the acceleration function is the derivative of the velocity function. The derivative of zero is zero.

4) Can the magnitude of a particles displacement be greater than distance traveled

Hell no!

5) Can the magnitude of a resultant be negative?

Magnitudes are always positive.

Martinez39s:
Yes. If the displacement function s(t) is continuous on a closed interval, say [a , b ] and it's differentiable on (a , b ) then there exists at least a time, say c, in (a , b ) such that:
This is called the Mean Value Theorem.

The instantaneous velocity can be zero. This is a no brainer na.

If the velocity of a particle is 0 then the acceleration is always zero. Remember that the acceleration function is the derivative of the velocity function. The derivative of zero is zero.

Hell no!

Magnitudes are always positive.

Waw...... Thanks boss.... I have something in pocket for my test....