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A cyclist travels away from their place of work They ride for 5 minutes at a constant speed. The cyclist stops at the store for 10 minutes. They then continue at a constant rate for another 15 minutes before reaching their final destination. Compare their distances from work to time travelled. What functions can represent each part of the cyclist journey in order

Options
Constant, linear, constant
Quadratic, constant, linear
Linear, constant, linear
Linear, constant, quadratic

1 answer

To analyze the cyclist's journey, we can break it down into three parts:

  1. First Segment (5 minutes at a constant speed): During this phase, the cyclist travels away from work at a constant speed. Since the speed is constant, the distance travelled plotted against time will be a linear function.

  2. Second Segment (10 minutes stop at the store): During this phase, the cyclist is stationary, meaning that there is no distance travelled. The function representing this part is constant (specifically, at zero distance).

  3. Third Segment (15 minutes at a constant speed): In this segment, the cyclist continues riding again at a constant speed. Similar to the first segment, this distance plotted against time will also be a linear function.

Putting this all together, the functions representing each part of the cyclist's journey are:

  • First segment: Linear
  • Second segment: Constant
  • Third segment: Linear

Therefore, the correct option is:

Linear, constant, linear