2.0 m
Since we've been told to ignore friction, then we can also ignore gravity since all it's doing is contributing to the normal force which is only of interest if we're paying attention to friction. So how fast will 13 N of force accelerate 34 kg of mass? Since a newton is kg*m/s^2 and we want to get m/s^2, a simple division should be able to cancel out the kg. So:
13 kg*m/s^2 / 34 kg = 0.382352941 m/s^2
The distance an object moves under constant acceleration is
d = 0.5 AT^2
So let's substitute the known values and calculate the distance.
d = 0.5 AT^2
d = 0.5 0.382352941 m/s^2 * (3.2 s)^2
d = 0.191176471 m/s^2 * 10.24 s^2
d = 1.957647059 m
Rounding to 2 significant figures gives 2.0 meters
