A car starting from rest accelerates at a constant rate of 5m per second square for some time. It then retards at a constant rate of -10m per second square and finally comes to rest. If the total taken time is 6 second. What is the maximum speed attained by the car ?

α = 5 m/s^2
β = -10 m/s^2
t = 6 s
Let maximum velocity be x
then x/α+x/β=t
Solving,
x=t/(1/α+1/β)
=αβt/(α+β)
= 5*(-10)*6 / (5+ (-10))
= -300/ -5
x = 60 meter per second.