Chapter 1, Problem 73A

To determine

The way to find the units of a, b and c.

Explanation of Solution

Given:

  $d=a{v}^2+bv+c$

Where, d is distance and has unit of meter, v is the velocity and has unit meter/second.

Calculations:

The quantities having same unit can be added. It means that unit of $a{v}^2$ , $bv$ and c is meter.

  $\begin{array}{l}d=a{v}^2\\ \left[\text{m}\right]=a\left[{\left(\text{m/s}\right)}^2\right]\\ a=\left[{\text{s}}^{\text{2}}\text{/m}\right]\end{array}$

  $\begin{array}{l}d=bv\\ \left[\text{m}\right]=b\left[\left(\text{m/s}\right)\right]\\ b=\left[\text{s}\right]\end{array}$

  $\begin{array}{l}d=c\\ \left[\text{m}\right]=c\end{array}$

Conclusion:

Thus, unit of a is ${\text{s}}^{\text{2}}\text{/m}$ , unit of b is $\text{s}$ and unit of c is m.