Where is the mouse located when it reaches top speed?

[doc2142]

Homework Statement

A mouse leaves a hole in the baseboard and runs along the wall in a straight line towards a
cupboard where cookies are stored, 12 meters from the hole. The mouse starts at rest and
maintains a constant acceleration of 0.1m/s2 before reaching top speed of 1 m/s, which it
maintains for the rest of the journey. When the mouse is 3 meters from the cookie
cupboard, a cat turns the corner and enters the kitchen, moving at 0.5 m/s. It immediately
begins to chases the mouse. The point where the cat enters is 14 meters from the cookie
cupboard.

Homework Equations

a) Where is the mouse located when it reaches top speed?
b) If the cat catches the mouse just as it reaches the cookie cupboard, what minimum
constant acceleration must the cat maintain?
c) How fast is the cat moving when it catches the mouse?
d) How much time has passed since the mouse left the hole?

The Attempt at a Solution

I found A by using Vf^2=V0^2+2a(Change in X)

I am stuck on B
I know first I need to know how long it takes for the mouse to reach the cupboard but i am confused on which formula to use. I know its 2 different equation one for before it reachs top speed when the acceleration is non constant, and one for when it is constent.

 

[davo789]

Well, you know at what distance from the cupboard the mouse reaches its maximum speed, so using this info you should be able to find out how long it takes it to reach the cupboard from 3 metres away. Then, using this time, you can find out what acceleration the cat must keep to reach the mouse just as it reaches the cupboard.

Using your solution to a), s=5m, which means that the mouse is traveling at its maximum speed when it is 3m from the cupboard (hint hint).