Question

Consider position [x] = L, time [t] = T, velocity [v] = L/T and acceleration [a] = L/T 2 . Find the exponent A in the equation v = a^2 t^ A /x

Answer 1

The exponent A in the equation is 3.

Step-by-step explanation:

v = a^2 t^ A /x

`v = (a^2t^A)/(x) \\\\vx = a^2t^A\\\\((L)/(T))(L) = ((L)/(T^2))^2(T)^A\\\\ (L^2)/(T)= ((L^2)/(T^4))(T)^A\\\\ (L^2)/(T) *(T^4)/(L^2) = (T)^A\\\\T^3 = T^A\\\\(T^3)/(T^3) = (T^A)/(T^3)\\\\T^(3-3) = T^(A-3)\\\\3-3 = A-3\\\\0 = A-3\\\\A = 3`

Therefore, the exponent A in the equation is 3.