Three students derive the following equations in which x refers to distance traveled, v the speed, a the acceleration (m/s^2), and t the time, and the subscript (0) means a quantity at time t=0: a) x=vt^2 + 2at, b) x=v0t+1/2at^2, and c) x=v0t+2at^2. Which of these could possibly be correct according to a dimensional check?

B) and C)

Explanation:

Dimensional check involves using the units of the fundamental quantities, like mass to verify the accuracy of a formula or model.

For this case, the quantities required are Length and Time. Their units are Metre (m) and Seconds (s) respectively.

Since x refers to Distance, v refers to velocity, a refers to acceleration and t refers to time,

A) x = vt² + 2at

=> m = (m/s * s²) + (m/s² * s)

m = ms + m/s

The units are unbalanced, hence, it is not dimensionally correct.

B) x = v₀t + 2at²

=> m = (m/s * s) + (m/s² * s²)

m = m + m

The units are balanced, hence, it is dimensionally correct.

C) x = v₀t + ¹/₂at²

=> m = (m/s * s) + (m/s² * s²)

m = m + m

The units are balanced, hence, it is dimensionally correct.