acceleration: how far will the car travel in 10 seconds?

[mathstresser]

A car accelerates at 2 m /s / s. Assuming the car starts from rest, how far will it travel in 10 s?
A) 2 m
B) 10 m
C) 40 m
D) 100 m
E) 200 m

after 1 second, it has gone 2 m.
after 2 seconds, I'm not sure... it has gone at least 2 m, but I think it has gone more.... I just can't figure out how much more...

Please help!

 

[tkhunny]

There are nice formulas for this sort of thing, but often one can gain quite a bit of information and experience just by playing with it.

It accelerates at 2 m/s/s.

It's velocity is:

0 m/s at 0 sec
2 m/s at 1 sec
4 m/s at 2 sec
6 m/s at 3 sec
...
20 m/s at 10 sec

It's distance from where it started is about:

1 m at 1 sec
1 m + 3 m at 2 sec
1 m + 3 m + 5 m at 3 sec
...

At some point, you may notice that this results in t² meters in t seconds.

 

[mathstresser]

Thanks!

 

[wjm11]

A car accelerates at 2 m /s / s. Assuming the car starts from rest, how far will it travel in 10 s?

Hi, Mathstresser,

D = d(initial position) + v*t (initial velocity times time) + (1/2)a*t^2 (.5 times acceleration times time squared)

Your initial position and velocity are both zero, so the first two terms drop out of this problem, and you’re left with

D = 1/2at^2

Hope that helps.