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

Answer:

The exponent A in the equation is 3.

Explanation:

v = a^2 t^ A /x

$v = \frac{a^2t^A}{x} \\\\vx = a^2t^A\\\\(\frac{L}{T})(L) = (\frac{L}{T^2})^2(T)^A\\\\ \frac{L^2}{T}= (\frac{L^2}{T^4})(T)^A\\\\ \frac{L^2}{T} *\frac{T^4}{L^2} = (T)^A\\\\T^3 = T^A\\\\\frac{T^3}{T^3} = \frac{T^A}{T^3}\\\\T^{3-3} = T^{A-3}\\\\3-3 = A-3\\\\0 = A-3\\\\A = 3$

Therefore, the exponent A in the equation is 3.