A car accelerates from rest at a constant rate α for some

A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

In Fig.
AA₁ = v_max. = αt₁ = βt₂
But t = t₁ + t₂ = v_max./α + v_max./β

= v_max.		1	+	1		= v_max.		α + β
		α		β				αβ

or, = v_max. = t		αβ
		α + β

		α² + β²		t
		αβ

		α² - β²		t
		αβ

	(α + β) t
	αβ