Help with Physics HW: Jane & Jim's Race to the Drop

[meandyou741]

Jane is going 3 m/s in a bike
at the end of the road is a 30 m drop.
jane passes jim
jim goes after jane 20 sec later, going 0.5 m/s^2 for 20 sec, then at a constant velocity until he reaches jane,
after jim has been traveling 8 sec, jane accelerates to 5/12 m/s^2 for 12 sec then continuing at a constant velocity.
if the road is 350m long, will jane and jim ever be at the same place?

 

[Delphi51]

Welcome to PF!
Ordinarily you must attempt the question before we can help, but since it is your first post I will try to get you started. It is very important to post the question exactly as given. Your question is missing the initial speed for Jim, so it cannot be solved as written.

A good way to work out a question like this is to make a sketch of the speed vs time graph for each rider. For the first 20 seconds, both are going at constant speed so you'll have horizontal lines on both graphs. Then Jim accelerates so you will have a line with a slope equal to his acceleration.

After sketching the graphs, figure out the areas under each section of the graphs. The area is the distance travelled. Then you are in a position to sum the distances up to each time on each graph and compare them. Perhaps a table showing time and the two distances would be the best way to organize the comparison.

 

[meandyou741]

The initial speed of jim is zero because he is at rest when jane passes him. And thank you for your reply. I'll make sure to post my work next time.