In physics, equations of motion describe how the position of an object changes over time. They often include terms such as initial position, velocity, and time, organized in a linear equation format. In our exercise, the equations for the two fish are each written as:
- Fish 1: \( x_{1} = -6.4 \, \text{m} + (-1.2 \, \text{m/s})t \)
- Fish 2: \( x_{2} = 1.3 \, \text{m} + (-2.7 \, \text{m/s})t \)
The equations are linear, which means they graph as straight lines, showing a constant velocity. Here, the velocity is the rate of change of position with respect to time, seen as the coefficient of \( t \):
- For Fish 1, the velocity is \(-1.2 \, \text{m/s}\).
- For Fish 2, it's \(-2.7 \, \text{m/s}\).
The negative sign indicates the fish are moving in a negative direction along the x-axis, which typically suggests they might be swimming downstream.