Chapter 2, Problem 61A

To determine

Explanation about the given quantities.

Answer to Problem 61A

The algebraic operations of $\Delta x$ and $\Delta t$ does not satisfy the property of the velocity.

Explanation of Solution

Introduction:

The addition and subtraction of two physical quantities is only possible, if both the quantities have same dimension.

The expression $\Delta x+\Delta t$ and $\Delta x-\Delta t$ shows the summation or difference of the displacement and time. The displacement and time have different dimensions, so the addition or subtraction of these quantities does not give the property of the velocity.

The product of the displacement and time has not the dimension of the velocity. The quotient of the time and displacement has not the dimension of the velocity.The expressions $\Delta x\times \Delta t$ or $\frac{\Delta t}{\Delta x}$ does not give the dimensions of the velocity.

Conclusion:

Thus, the algebraic operations of $\Delta x$ and $\Delta t$ does not satisfy the property of the velocity.