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

Let's analyze each equation dimensionally to determine which one is possibly correct.(a) - Distance traveled (x) has a dimension of length (L).- Speed (v) has a dimension of length per unit time (L/T).- Time (t) has a dimension of time (T).- Acceleration (a) has a dimension of length per unit time squared (L/T^2).Substituting the dimensions into the equation:- Simplifying:- The dimensions on the right side do not match the dimension of length (L) on the left side. Therefore, equation (a) is not dimensionally correct.(b) - Distance traveled (x) has a dimension of length (L).- Initial speed ( ) has a dimension of length per unit time (L/T).- Time (t) has a dimension of time (T).- Acceleration (a) has a dimension of length per unit time squared (L/T^2).Substituting the dimensions into the equation:- Simplifying:- The dimensions on the right side match the dimension of length (L) on the left side. Therefore, equation (b) is dimensionally correct.(c) - Distance traveled (x) has a dimension of length (L).- Initial speed ( ) has a dimension of length per unit time (L/T).- Time (t) has a dimension of time (T).- Acceleration (a) has a dimension of length per unit time squared (L/T^2).Substituting the dimensions into the equation:- Simplifying:- The dimensions on the right side match the dimension of length (L) on the left side. Therefore, equation (c) is dimensionally correct.In conclusion, both equations (b) and (c) are dimensionally correct.