Question

one of these representations is not like the others. tap on the one that doesnt belong.

Explanation:

Step1: Analyze the first table

The first table shows the relationship between time \(t\), horizontal displacement \(d_x\) and vertical displacement \(d_y\). The horizontal displacement \(d_x = 8t\) (linear relationship with time, constant horizontal velocity \(v_x=\frac{\Delta d_x}{\Delta t}=8\ m/s\)), and the vertical displacement \(d_y=- 4.9t^{2}\) (quadratic relationship with time, which is consistent with the formula \(y = v_{0y}t-\frac{1}{2}gt^{2}\), here \(v_{0y} = 0\) and \(g = 9.8\ m/s^{2}\)).

Step2: Analyze the second table

The second table shows the relationship between time \(t\), horizontal velocity \(v_x\) and vertical velocity \(v_y\). The horizontal velocity \(v_x\) is constant (\(v_x = 12\ m/s\)), and the vertical velocity \(v_y=-9.8t\) (linear relationship with time, which is consistent with the formula \(v_y=v_{0y}-gt\), here \(v_{0y} = 0\) and \(g = 9.8\ m/s^{2}\)).

Step3: Analyze the vector - diagram

The left - side vector - diagram (with the note "Arrows represent velocity vectors") is consistent with the motion described by the two tables (constant horizontal velocity and linearly - changing vertical velocity). The right - side vector - diagram (with the note "Arrows represent acceleration vectors") is not consistent. In projectile motion (assuming no air - resistance), the acceleration is constant (\(a=-g=- 9.8\ m/s^{2}\) in the vertical direction and \(a_x = 0\) in the horizontal direction), and there should be no change in the acceleration vector with time. But the right - side diagram (with the note "Arrows represent acceleration vectors") seems to imply a non - constant acceleration (if we consider the length of the arrows in a wrong way, while in reality, for projectile motion acceleration is constant).

Answer:

The vector - diagram with the note "Arrows represent acceleration vectors" (the right - side vector - diagram in the lower part of the picture) is the one that doesn't belong.