General questions- acceleration and velocity

[joe215]

I have some general acceleration and velocity questions...

Can average velocity and instantaneous velocity be equal for a specific type of motion?

Can instantaneous velocity ever be greater in magnitude than average velocity?

If an object has zero velocity, is its acceleration necessarily zero at that instant?

Can the sign of acceleration ever be positive for an object that is slowing down?

Help is appreciated! Thanks!

 

[Varnick]

I'll number your questions, and answer them one by one.

1. If you have constant velocity between two points, the instantaneous velocity will be equal to the average.

2. Yes. If, for example, you had an object traveling at 10m/s for 1 second, then 2m/s for 5 seconds, the instantaneous velocity at t=1 is 10, but the average velocity is 20/6.

3. Yes, if velocity is negative, but accelerates and becomes positive, then it must pass v=0, but there is still acceleration. (You can have sloped lines through v=0)

4. The sign of a vector is arbitrary. For instance, when working with projectiles, you can say that g, acceleration due to gravity is either positive or negative. It doesn't matter which way is positive and which is negative, as long as you are consistent.

Hope this was helpful,

V