A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate `beta` to come to rest. If the total time elapsed is t, the maximum velocity acquired by the car is given by :

Options

A. `(abt)/(a+b)`
B. `(a^(2)t)/(a+b)`
C. `(at)/(a+b)`
D. `(b^(2)t)/(a+b)`

Answer

a

Explanation

Acceleration =+a, for time `t_(1)`
From initial to maximum velocity.
`v_("max")=0+at_(1)`
`t_(1)=(v_("max"))/(a)`
It then decelerates with constant rate b and stops in time `t_(2)`
`0=v_("max")-bt_(2)`
`t_(2)=(v_("max"))/(b)`
If the total time is given t,
`t=t_(1)+t_(2)`
`v_("max")=(abt)/((a+b))`