A truck is stopped at a traffic light. The moment the light turns green, it begins to accelerate constantly at 3.1m/s^2. A cyclist approaching the truck from behind with a constant velocity of 10m/s was 7.5m behind the truck when the lights turned green.
1)How much time elapses between the light turning green and the bike passing the truck?
2)How long does it take for the truck to re-pass the bike?
3)How far has the truck traveled from the lights when it re-passes the bike?
This is a Kinematics question, so all the Kinematic Equations are applicable, which are as follows:
The Attempt at a Solution
When the one passes the other, they would both have to be at the same position. I made their initial positions as "x" for the truck, and "x-7.5" for the bike. As the bike will gain on and pass the truck until they have the same speed, I know that the speed they will have when the bike first passes the truck will be less than or equal to the bike's initial speed. Unfortunately, I'm having difficulty seeing how the Kinematic Equations can get me started here. I get the feeling it'll involve some sort of quadratic, but I'm unsure of how to properly make the two aforementioned starting points of the truck and bike into a quadratic form, and from there how to derive additional values for my three Kinematic Equations.