## Physics (10th Edition)

$a,b,c,f$
To prove which equations the units are consistent, we need to substitute each variable by its units and simplify. a) $x(m)=v(m/s)*t(s)$ $m=\frac{m}{s}*s$ $m=\frac{m*s}{s}$ $m=m$ This one is consistent b) $x(m)=v(m/s)*t(s)+\frac{1}{2}*a(m/s^2)*(t(s))^2$ $m=\frac{m}{s}*s+\frac{1}{2}*\frac{m}{s^2}*s^2$ $m=\frac{m*s}{s}+\frac{1}{2}*\frac{m*s^2}{s^2}$ $m=m+\frac{1}{2}m=\frac{3}{2}m$ This one is consistent c) $v(m/s)=a(m/s^2)*t(s)$ $\frac{m}{s}=\frac{m}{s^2}*s$ $\frac{m}{s}=\frac{m*s}{s^2}$ $\frac{m}{s}=\frac{m}{s}$ This one is consistent d) $v(m/s)=a(m/s^2)*t(s)+\frac{1}{2}*a(m/s^2)*(t(s))^3$ $\frac{m}{s}=\frac{m}{s^2}*s+\frac{1}{2}*\frac{m}{s^2}*s^3$ $\frac{m}{s}=\frac{m*s}{s^2}+\frac{1}{2}*\frac{m*s^3}{s^2}$ $\frac{m}{s}=\frac{m}{s}+\frac{1}{2}ms$ This one is not consistent e) $(v(m/s))^3=2*a(m/s^2)*(x(m))^2$ $\frac{m^3}{s^3}=2*\frac{m}{s^2}*m^2$ $\frac{m^3}{s^3}=2*\frac{m*m^2}{s^2}$ $\frac{m^3}{s^3}=2\frac{m^3}{s^2}$ This one is not consistent f) $t(s)=\sqrt \frac{2*x(m)}{a(m/s^2)}$ $s=\sqrt {2*m*\frac{s^2}{m}}$ $s=\sqrt {2*\frac{m*s^2}{m}}$ $s=\sqrt {2*s^2}$ $s=\sqrt 2s$ This one is consistent