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According to the principle of dimensional homogeneity,
Dimension of v = Dimension of At² = Dimension of Bt
Now,
• Dimension of A = (Dimension of v)/t²
→ [LT⁻¹] / [T²]
→ [LT⁻¹] × [T⁻²]
→ [LT⁻³]
→ [M⁰L¹T⁻³]
• Dimension of B = (Dimension of v)/t
→ [LT⁻¹] / [T]
→ [LT⁻¹] × [T⁻¹]
→ [LT⁻²]
→ [M⁰L¹T⁻²]
Hence, the dimension of A is [M⁰L¹T⁻³] and dimension of B is [M⁰L¹T⁻²].
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