Unit conversion

Convert 1 m/s² into gal (cm/s²) using dimensional analysis

1 m/s² = 100 gal (cm/s²). Acceleration is [L T⁻²], so only the powers of mass, length and time decide the factor.

Length×10²1 m = 100 cm

Time²×1s in both systems

1 m/s² 100 gal (cm/s²)

Working

Step by step

The dimension of accelerationAcceleration has the dimensions [L T⁻²]. Only the powers of M, L and T matter for the conversion.
The conversion ruleA quantity with dimensions [M^a L^b T^c] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in the new system. Here n₂ = n₁ [L₁/L₂] [T₁/T₂]⁻².
The size of each base unitL: 1 metre (m) is 100 centimetre (cm). T: 1 second (s) is the same in both systems.
Put the numbers inn₂ = 1 [1 m / 1 cm] [1 s / 1 s]⁻²
Work out each bracket[L₁/L₂] = 100; [T₁/T₂]⁻² = 1⁻² = 1
Multiplyn₂ = 1 × 100 × 1 = 100
The answer1 m/s² = 100 gal (cm/s²)

Questions

How do you convert m/s² to gal (cm/s²)?

Acceleration is [L T⁻²]. Multiply by the ratio of each base unit raised to its power in the dimension. That gives 1 m/s² = 100 gal (cm/s²).

What is 1 m/s² in gal (cm/s²)?

1 m/s² = 100 gal (cm/s²).