If the car speeds up at a steady 1.6 m/s2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

Based on internet sources, the basic formulas are: v^2/r = (at)^2/r = a ==> at^2 = r ==> t = sqrt(r/a). 

Assuming the missing units are mutually compatible, as in the following example, they don't need to be known. 
Acceleration = 1.6 cramwells/s^2 
Radius = 150 cramwells 
t = sqrt(150/1.6) = 9.68 s.

I hope this helps.