When log s (as ordinate) is plotted against t (as abscissa) on linear paper, the graph is a straight line with
slope of -2.1 and intercept of 1.5. Express the relationship between s and t as s = Aekt . If s represents a
distance in meters and t a time in seconds, what are the units of A and k?
In the equation s = Aekt, the units of A and k can be determined by analyzing the units of each term in the equation.
Considering that s represents a distance in meters and t represents a time in seconds, we can determine the units of A and k as follows:
1. Units of A:
Since s represents a distance in meters, the units of A must also be in meters to ensure that both sides of the equation have compatible units.
2. Units of k:
For s = Aekt, the constant k is the exponent on the base e. The exponential function e is dimensionless, meaning it does not have any units associated with it. Therefore, k must have units of inverse seconds (1/s) to ensure that the units on the right side of the equation (s) match the units on the left side of the equation.
To summarize, the units of A are meters (m) and the units of k are inverse seconds (1/s).
To determine the units of A and k in the equation s = Aekt, we need to analyze the units of each term separately.
In the given equation, s represents a distance in meters, and t represents time in seconds.
Let's break down the units for each term:
- s: Distance (meters)
- A: Constant
- e: Exponential constant (dimensionless)
- k: Rate constant (per second)
- t: Time (seconds)
Since the left side of the equation represents a distance in meters, the right side of the equation should have the same units.
Considering the right side, Aekt, we can deduce the units of A and k:
- The constant A must have the units of meters to cancel out the units of e and t when multiplied together.
- The exponent kt needs to result in a dimensionless quantity.
Therefore, the units of A should be meters, and the units of k should be inverse seconds (s^-1).
To summarize:
- The units of A are meters.
- The units of k are inverse seconds, s^-1.
So, the relationship between s and t can be expressed as s = Aekt, where A has units of meters and k has units of inverse seconds, s^-1.