Final answer:
Only equation (b), x = v0t + 1/2 at², passes the dimensional check, as it is the only one with consistent dimensions of meters on both sides of the equation. Therefore, only equation (b) x = v_0t + 1/2 at² is potentially correct according to a dimensional check.
Step-by-step explanation:
When conducting a dimensional check for the equations provided by three students to describe the distance traveled (x), with given variables for speed (v), acceleration (a), and time (t), we are looking to ensure that the dimensions are consistent on both sides of the equation.
Equation (a) x = vt² + 2at is incorrect because the units do not match: on the left-hand side we have a dimension of distance (m), and on the right, we have m/s multiplied by s², which is ², plus meters per second squared multiplied by seconds, which gives us meters (m); the two terms are not dimensionally consistent.
Equation (b) x = v_0t + 1/2 at² is dimensionally consistent: on the left-hand side, we have meters (m), on the right, we have meters per second (m/s) multiplied by seconds (s) plus meters per second squared (m/s²) multiplied by the square of seconds (s²), both resulting in meters (m).
Equation (c) x = v_0t + 2at² is incorrect because the second term has dimensions of meters per second squared (m/s²) times the square of seconds (s²), which gives meters squared per second squared (m²/s²), not meters (m).