Valid Expressions are; t = ∛(d²/va), a = d/t², a = √(vd/t³), v = at
while the Invalid expressions are; v = a/t and d = at
Explanation:
Given expressions
1) v = a/t
2) t = ∛(d²/va)
3) d = at
4) a = d/t²
5) a = √(vd/t³)
6) v = at
First we get our units of parameters
V = m/s, t = sec, d = m, a = m/s²
so
1)
v = a/t
we substitute in our units of parameters
v = m/s² / s = m/s² × 1/s = m/s³
v ≠ m/s³
therefore it is false
2)
t = ∛(d²/va)
we substitute
t = ∛(m² / m/s × m/s²)
t = ∛(m² / m²/s³)
t = ∛(s³)
t = s
correct, the expression is true
3)
d = at
we substitute
d = m/s² × s
d = m/s² × s/1 = ms/s² = m/s
d ≠ m/s (because d = m)
so expression is false
4)
a = d/t²
we substitute
a = m / s² = m/s²
correct
the expression is true
5)
a = √(vd/t³)
we substitute
a = √(m/s×m / s³) = √(m²/s / s³) = √(m²/s × 1/s³) = √(m²/s⁴) = m/s²
so a = m/s²
correct
the expression is true
6)
v = at
we substitute in the units
v = m/s² × s = m/s² ×s/1 = ms/s² = m/s
v = m/s
correct
the expression is correct
