If you think about it: let's say the given is X=0 at t=0. We can use the table below.
time(t) |
distance (x) |
0s |
0 |
1s |
3 |
2s |
9 |
3s |
18 |
Now, we can see that the distance increases at an exponential rate, so these kinds of data would not be a result of a particle moving at a constant velocity. If the velocity is constant at 3m/s, our distance would be 0,3,6,9. We can use this kind of thinking for choice 3. If the velocity is constant at 6m/s, then the distance would 0,6,12,18 in 4 seconds. We have now eliminated choices 2 and 3.
To eliminate between choices 1 and 4, we can use one of our kinematic equations (x=vi*t+0.5*a*t^2). At t = 3, our x should be 18 if our initial velocity is equal to 0.
x=0+0.5*(3m/s^2)(3s)^2
x=27/2
x is not equal to 18 which means choice 1 is false. This makes choice 4 the only correct answer. Also, we know our answer is correct because the velocity increases exponentially as time t increases.