Final answer:
In dimensional analysis for the equation d = st, speed (m/s) multiplied by time (s) cancels out the seconds, leaving meters on both sides. This validates that the distance (d) has the same units as the product of speed (s) and time (t).
Step-by-step explanation:
To show that each side of the equation d = st has the same units, we need to conduct a dimensional analysis. The variable d stands for displacement or distance, which is typically measured in meters (m). The variable s represents speed or velocity, which has units of meters per second (m/s), and t represents time, commonly measured in seconds (s). When we multiply speed (s) by time (t), the unit of seconds (s) from the time cancels out the unit of seconds (s) in the denominator of the velocity, leaving us with meters (m), which is the same unit as displacement (d).
This can be represented in terms of units as follows:
m = (m/s)(s)
Since the units of time cancel out, we are left with meters on both sides of the equation, demonstrating that the units match and validating that the equation is dimensionally consistent.