A skateboarder starts from rest and moves down a hill with constant acceleration
ID: 1953035 • Letter: A
Question
A skateboarder starts from rest and moves down a hill with constant acceleration in a straight line, traveling for 6 seconds. In a second trial, he starts from rest and moves along the same straight line with the same acceleration for only 2s. How does his displacement from his starting point in this second trial compare with that from the first trial? (a) one-third as large (b) three times larger (c) one-ninth as large (d) nine times larger (e) 1/sqrt(3) times as large.
My thought process on this was as follows: We know the difference in times, everything else in the problem is similar. So I took a look at the kinematic equations and decided that since we're talking about displacement (displacement being xf - xi) I chose to work with xf = xi + vxit + (1/2)axt2
Xi and vxit are zero so really we're working with how 1/2axt2
when t=6, 1/2axt2 = 18ax
when t=2, 1/2axt2 = 2ax
so 2ax/18ax = 1/9, so the answer would be choice (c). Does this logic make sense and is it correct? Thanks!
Explanation / Answer
yes you are right, the choice should be c 18/2 =9