Cornering

[AppleBuggie]

I've had my 1300 06 AT Vitz for about 2 months now and I've noticed a couple things. Since this is the best place to ask:

I find that the car does not accelerate right away at times. For example on overtaking someone, I'd want to pump the gas a little to go into another 'gear' and the car just takes it's own sweet time. A friend of mine said it's the VVT is that true?

Also in cornering, the car feels as if it slows down when turning corners. I'm moving at an ok speed, I go to break a little, turn and exit out the corner and i get nothing, it just slows down. Is it because of the whole 1.3 litre thing? Is it becuz itz less power? Is this quite normal?