Question

Car a starts from rest and speeds up with constant accelleration until it reaches its max speed. Car b starts from rest, at the moment car a is at max speed, and speeds up with constant acceleration. How much time elapses between when car b starts moving, and car b passes car a.

I have tried to solve using kinematic equations but nothing seems to work.

Car A
vA
aA
tA

Car B
vB
aB
tB

Answer 1

Da = Db same distance
total time a = time b + delay b
we want time b

Car A
accelerate phase:
vi = aA delayb
Di = .5 aA delayb^2
constant speed phase
Da = Di + vi t
= .5 aA delayb^2 + aA delayb timeb

Car B
Db = .5 aB timeb^2

now Da=Db so
.5 aA delayb^2 + aA delayb timeb = .5 aB timeb^2

Now you really need to know what that max speed vi is to get the time car A accelerates which is delay B
or just put it in here as
delayb = vi/aA

.5 vi^2/aA + vi timeb = .5 aB timeb^2
solver quadratic for timeb