Scooby Doo is being chased by the Phantosaur! Scooby Doo very quickly accelerates at 6 ms^-2 to his top velocity of 3 ms^-1. Scooby Doo, having been chased by lots of ghosts, is good at running and can maintain this velocity. The Phantosaur accelerates at 3 m s^-2, and has a top velocity of 6 ms^-1.

However, the Phantosaur can only maintain such a high velocity for 1 s before getting tired and slowing down at a rate of 1 m s^-2. Will the Phantosaur eat Scooby Doo?

This is a tricky intersection problem, because Scooby Doo and the Phantosaur speed up, maintain a constant velocity and (in the case of the Phantosaur) slow down. Therefore, we have to solve this in sections

i. How long does it take Scooby to accelerate to his top speed and how far has he traveled?

ii. How long does it take the Phantosaur to accelerate to his top speed and how far does it travel?

During the time it takes the Phantosaur to get up to its maximum velocity, how far has Scooby ran?

iii. The Phantosaur can only maintain the high velocity for 1 s. After this 1 s, how far has it ran, and how far has Scooby ran?

iv. Finally Scooby maintains a constant velocity, while the Phantosaur slows down. What are the equations for distance traveled by both Scooby and the Phantosaur while the Phantosaur is decelerating?

At any point in the previous steps was the Phantosaur ahead of Scooby Doo?