Based on these units, select any of the following expressions that could be valid expressions?v=a/tt=3√d2/vad=ata=d/t 2a=√vd/t3v=at

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

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