$$ \begin{array}{l} \mathrm{V}_{\mathrm{A}}=\frac{\mathrm{d}_{\mathrm{A}}}{\mathrm{t}} ; \mathrm{V}_{\mathrm{B}}=\frac{\mathrm{d}_{\mathrm{B}}}{\mathrm{t}} \\ \mathrm{d}_{\mathrm{A}}=80 \mathrm{~m} \text { and } \mathrm{d}_{\mathrm{B}}=100 \mathrm{~m} \\ \mathrm{~V}_{\mathrm{A}}=\frac{80}{\mathrm{t}} ; \mathrm{V}_{\mathrm{B}}=\frac{100}{\mathrm{t}} \Rightarrow \mathrm{V}_{\mathrm{A}}<\mathrm{V}_{\mathrm{B}} \cdot \mathrm{B}^{\prime} \text { is faster than }^{4} \mathrm{~A}^{\prime} . \end{array} $$

Understanding the distance-time relationship is critical when studying motion.
It tells us how the distance traveled by an object connects with the time taken to cover that distance. To visualize this relationship, you can imagine walking a certain path: the longer you walk (time), the more ground you cover (distance). However, if you walk faster, you cover more ground in less time.

This concept is fundamental in physics for analyzing how objects move from one point to another. In the context of our exercise, both objects A and B traveled different distances in the same amount of time, t. Object A covered 80 meters, while Object B traveled 100 meters. As they moved in the same time frame, we can easily compare their speeds to find out which one is faster by using the velocity formula.

Velocity is the rate at which an object changes its position. It's a vector quantity, meaning it has both magnitude and direction, but for simplicity, we often just look at the magnitude (speed) when comparing two objects like A and B.

The standard velocity formula is:
\[\begin{equation}Velocity (V) = \frac{Distance (d)}{Time (t)}\end{equation}\]By applying this formula, we calculated the velocities for A and B as \[\begin{equation}V_A = \frac{80 m}{t}\end{equation}\]and\[\begin{equation}V_B = \frac{100 m}{t}\end{equation}\]respectively. With the distances known and time being constant, velocity becomes directly proportional to distance - an essential takeaway for understanding motion dynamics.

When comparing velocities, it's crucial to consider all aspects of the velocity formula. Since time, t, is the same for both objects A and B in our exercise, comparing their velocities comes down to looking at the distances they traveled.

By only comparing the distance part of the velocity equation for each object:\[\begin{equation}V_A = \frac{80}{t}\end{equation}\]and\[\begin{equation}V_B = \frac{100}{t}\end{equation}\]we see that since 100 m is greater than 80 m, V_B must be greater than V_A, assuming 't' is positive and the same for both A and B. This comparison tells us that object B is faster than object A - a conclusion that can be reached without even knowing the actual time it took for the movement, which showcases the power of algebraic reasoning in physics.