A remote control car starts moving in a straight line from a fixed point. The velocity in metres per second is given by the formulai)

v = 3t^{2}- 4t - 8

what is the initial acceleration?

So for this question I assume you differentiate, to get your acceleration equation:a = 6t - 4Then I'd assume you put the t at 0, to get the initial acceleration, because that is what initial means - at time 0. But that just gives me -4 acceleration, which doesn't seem right to me.

ii)how far does the car travel in the third second?

I'd assume you integrate, on this one, because you want the distance formula:d = tThe answer I got from this was that the constant was 15^{3}- 2t^{2}- 8t + c

,because I set the letter t to 3, and, yup.

But then, the distance turned out to equal, um, 0. Which also didn't seem right.

What am I doing wrong, in both questions, that I end up with these weird answers??