Answer:
1) t=cubed rootinside d^2/va
2) v=at
3) a=sqrt vd/t^3
6) a=d/t^2
Step-by-step explanation:
We are given the following:
In the SI unit system, time (t) is measured in seconds(s),
distance (d) is measured in meters(m)
velocity (v) is measured in meters per second[tex](ms^{-1})[/tex], and
acceleration (a) is measured in meters per second squared[tex](ms^{-2})[/tex].
[tex]\text{Velocity} = \dfrac{\text{Distance}}{\text{Time}}\\\\\text{Acceleration} = \displaystyle\frac{\text{Change in velocity}}{\text{Time}}\\\\1)\\\\t = (\dfrac{d^2}{va})^{\frac{1}{3}}\\\\t = (\dfrac{m^2}{ms^{-1}ms^{-2}})^{\frac{1}{3}}\\\\t = (s^3)^{\frac{1}{3}}\\\\t = s\\2)\\v = at\\v = ms^{-2}\times s\\v = ms^{-1}\\\\3)\\a = \sqrt{\frac{vd}{t^3}}\\\\a = \sqrt{\frac{(ms^{-1})(m)}{s^3}}\\\\a = \sqrt{m^2s^{-4}} = ms^{-2}\\\\6)\\a = \frac{d}{t^2}\\\\a = \frac{m}{s^2} = ms^{-2}[/tex]
Thus, valid expressions are
1) t=cubed rootinside d^2/va
2) v=at
3) a=sqrt vd/t^3
6) a=d/t^2