Sketch the velocity-time graph for each cyclist. Equate the distances travelled to analyze the motion and calculate when the cyclists take over each other.

Using the TI-Nspire calculator, you can plot the velocity-time graphs for both cyclists. Examine the velocity-time graphs to understand the motion of each cyclist. Look for key features such as the initial velocity, acceleration, and any changes in direction. Finding specific values, such as the time when two cyclists meet or the time it takes for one to catch up with the other, you can set up equations based on the information from the graphs. Use the calculator’s equation-solving capabilities to find these values. Once you have obtained numerical solutions from your calculations, interpret the results in the context of the problem. Make sure your answers align with the physical situation described in the problem statement.