The velocity of a particle depends upon time as $v = a + bt + ct^2$; if the velocity is in m/sec, the unit of

Question

The velocity of a particle depends upon time as $v = a + bt + ct^2$; if the velocity is in m/sec, the unit of $a$ will be:

Accepted Answer

1. **Principle of Homogeneity:** According to the principle of dimensional homogeneity in physics, only physical quantities having the same dimensions (and units) can be added or subtracted. In an equation like $v = a + bt + ct^2$, every term on the right-hand side ($a$, $bt$, and $ct^2$) must have the same dimensions and units as the term on the left-hand side ($v$). 
2. **Identify Units:** The unit of velocity $v$ is given as m/sec.
3. **Determine Unit of 'a':** Since $a$ is added directly to terms that equate to velocity, the unit of $a$ must be identical to the unit of velocity. Therefore, the unit of $a$ is m/sec.

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