Answer:
(a) [tex]\frac{1}{2}mv^2 = \frac{1}{2}mv_0^2 + mgh\\\frac{1}{2}(kg)(\frac{m^2}{s^2}) = \frac{1}{2}(kg)(\frac{m^2}{s^2}) + (kg)(\frac{m}{s^2})(m)\\\frac{kg m^2}{s^2} = \frac{kg m^2}{s^2}[/tex]
This equation is correct. In fact, this equation comes from the conservation of energy.
(b) [tex]v = v_0 + at^2\\\frac{m}{s} = \frac{m}{s} + \frac{m}{s^2}s^2\\\frac{m}{s} = \frac{m}{s} + m[/tex]
The units in both sides does not match. So this equation cannot be correct.
(c) [tex]ma = v^2\\(kg)(\frac{m}{s^2}) = \frac{m^2}{s^2}[/tex]
The units in both sides does not match. So this equation cannot be correct.
