I’m in a physics class (AP Physics B, but also IB Standard-Level Physics), and for every chapter we are assigned a homework assignment on the University of Texas Austin website, which has a homework service dubbed “Quest Learning and Assessment”. Normally, the homeworks are quite fun to figure out, and the questions are challenging, etcetera. But sometimes the “correct” answers are tricky to come up with or just stupid and wrong. For instance, there is one question that reads “Before coming to Earth, your teacher was on planet Krypton where there was almost no atmosphere. Your teacher observed and plotted the position of a projectile at constant intervals of 0.24 s , as shown in the figure.”
“The ball is in free-fall and there is no acceleration at any point on its path. Calculate the vertical acceleration due to the gravity of planet Krypton on the projectile. Answer in units of m/s2.”
Anyone with even an extremely conceptual grasp on Physics can tell you that this is a negative acceleration. The problem does not ask for the magnitude. It does not say that up is considered a negative direction. It follows, then, that the acceleration is negative, because it moves the velocity towards the negative direction. However, the service wants a positive answer for some reason. Don’t ask me why; there is absolutely no reason that it should be positive. For those who are wondering how to solve this, below is my work for the problem:
s = ut + (1/2)·a·t2 ( or ) ∆x = v0·∆t + (1/2)·a·∆t2
For the sake of problem-solving-speed, I consider the second half of the parabola, because it means the initial velocity is zero and we won’t have to deal with the quadratic formula.
Displacement (s or ∆x) on the first half of the parabola is 70 m, so that means on the second half it’s -70 m.
Time (t or ∆t) is (0.24 s)*7 = 1.68 s (the intervals are .24s apart, and there are seven intervals in one half of the parabola).
We plug in and use ALGEBRA.
(-70 m) = (0 m) + (1/2)(a)(2.8224 s2)
(-70 m)*2 = (a)(2.8224 s2)
(-140 m) = (a)(2.8224 s2)
(-140 m)/(2.8224 s2) = a
a = -49.60317460317 m/s2 ≈ -49.603 m/s2
And then, for some reason, we find the absolute value, and +49.603 m/s2 is our answer.