Question

If the velocity of a particle is given by v = a + b/t + Ct^2, what is the unit of b?

Answer 1

The velocity equation \(v = a + \frac{b}{t} + Ct^2\) implies that the unit of \(b\) must be in meters times seconds (\(m \cdot s\)).

Here's a breakdown:

- The term \(a\) represents the initial velocity, and its unit is \(m \cdot s^{-1}\).

- The term \(\frac{b}{t}\) involves a division by time (\(t\)), so \(b\) must have units of \(m \cdot s\).

- The term \(Ct^2\) represents an acceleration term, and \(C\) must have units of \(m \cdot s^{-3}\) to ensure that the entire expression has consistent units.

So, the unit of \(b\) is \(m \cdot s\).

Answer 2

The unit of the term 'b' in the velocity equation is meters (m), determined by ensuring that each term has the same unit of velocity, meters per second (m/s).

Step-by-step explanation:

The unit of the term b in the velocity equation v = a + b/t + Ct^2 can be determined by dimensional analysis. In this equation, v represents velocity and its unit is meters per second (m/s). The time t has units of seconds (s). Because the term b/t must have the same unit as velocity to be summed algebraically, the unit of b divided by the unit of t (s) must result in meters per second (m/s). Therefore, the unit of b must be meters (m).