find velocity and distance bet. A & B in the terms of alpha , beta & T ...

max acceleration = ?

max retardation  = ?

let distance between A and B = S

total tome taken = T

 

let car accelarate at max acceleration for t1 sec covering s1 and decelerate for t2 sec covering s2

both at max magnitudes.

thus

t1 + t2 = T

s1 + s2 = S

 

for first accelerating part,

max velocity attained will be at end of t1 time,

thus using first equation of motion, Vmax = v1 = ?.t1  (as initial velocity is zero)

and using second equation of motion, s1 = 1/2?.t1²

and using third eqation of motion, v1 = (2?.s1)^1/2

 

in second lap of journey while decelerating:

using first eq. of motion,

v1 = ?.t2 (as final velocity will now be zero)

thus ?.t1 = ?.t2

 

similarly using third eq. of motion,

v1 = (2?.s2)^1/2

 

thus from earlier,

?.s2 = ?.s1

 

thus from these two S and v1 can be derived in terms of T