What distance does an object travel if it accelerates uniformly from rest at a rate of 6m/s/s for 6s? What is the car's displacemtn if the acceleration is directed to the north?

displacement = 0.5 * acceleration * time^2; plug in the values and you're done.

each second the object travels an additional 6m than the prevvious second: 6+12+18+24+30+36= 126m

Mathheadincloud has it right.

In the first second the object actually travels just 3 m, not 6. After that it does inded go 6 m further each second than it did the second before:

3m + 9m + 15m +... +33m.

But this is a strange way to try to solve this problem. It's easiest to just use the formula d = 1/2 a t^2.

Serves me right for doing calcs in my head after 39 years of working in a school. You are correct, the speed is zero starting and 6 after one second so its mean speed was 3, entered the next second at 6 ending at 12, mean of 9, 12 to 18 with a mean of 15, mathhead are you following this? I think mathead is maybe a middle schooler or freshman so I tried to answer him the way we do in 8th grade, freshman ISP