Question

Two children are playing a game where they run towards each other and see who can reach a toy that is somewhere between them. In the beginning, Charlie is 23.7 m away from the toy, running towards it at a speed of 0.770 m/s, and is speeding up. At the same time, Amy is 12.5 m away from the toy, is running towards it in the opposite direction as Charlie at a speed of 2.70 m/s, and is slowing down. Charlie is increasing his speed by 1.22 m/s every second and Amy is decreasing her speed by 0.25 m/s every second. Your primary goal is to find out who reaches the toy first.

ii. Graphical Approach:

1. Present a graphical interpretation of the problem to solve: Neatly draw three blank graphs on one piece of graphing paper so that the horizontal axes are all aligned (time axes), making your graphs as large as possible.

2. It is typically easier to start with the acceleration graph to find the velocity graph than the other way around. Start this one with an acceleration vs. time graph – draw the acceleration graph for each child on a single graph. Explain your choices in detail.

3. Use the acceleration graphs you created to make the velocity vs. time graphs for both children (on the same graph). You will need to consider the initial velocity information for each child. Explain your choices in detail.

4. Use the velocity graphs you created to make the positon vs. time graphs for both children (again, on the same graph). You will need to consider the initial position information for each child. Also draw a position vs. time graph for the toy on the same graph. Explain your choices in detail.

5. Use the position vs. time graph to determine who reaches the toy first.

Answer 1

I don't have graph paper so I drew then on a regular rulled page. I markerd the measures.