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Chapter 1: Problem 151

Equation of force \(F=a t+b t^{2}\) where \(F\) is force in Newton \(t\) is time in second, then write unit of \(\mathrm{b}\). (a) \(\mathrm{Ns}^{-1}\) (b) \(\mathrm{Ns}^{2}\) (c) \(\mathrm{Ns}\) (d) \(\mathrm{Ns}^{-2}\)

Short Answer

Expert verified
(d) \(\mathrm{Ns^{-2}}\)

Step by step solution

01

Analyze the equation

We have the equation \(F = at + bt^2\). Let's analyze the units of the left-hand side (LHS) and right-hand side (RHS) of the equation.
02

Find the units of the LHS

On the left-hand side, we have the force F, which is given in Newton (N). So, the units of LHS are N.
03

Find the units of each term on the RHS

On the right-hand side, we have two terms: \(at\) and \(bt^2\). 1. For the term at, we know the time t has the unit seconds (s). Since the term at has the same dimension as force, the constant a must have the units of Ns^{-1}. 2. For the term bt^2, we know the time t has the unit seconds (s). Thus, the units of t^2 are \(s^2\).
04

Find the units of constant b

Since the term bt^2 has the same dimension as force, the constant b must have the units that, when multiplied by \(s^2\), result in the force unit N. So, the units of the constant b should be \(\frac{N}{s^2}\). Thus, the correct answer is: (d) \(\mathrm{Ns^{-2}}\)

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