The correct options are
A a: m/s
b: m/s2
B a: cm/s
b: cm/s2
Given,
v = a + bt + ct2
v has the units of speed.
Two quantities can be added only if they have the same units.
Hence, a and bt has units of speed.
Given, t is time. Hence, b has the units of speed per unit time.
So, from the options, units of a can be m/s or cm/s.
And, units of b can be m/s2 or cm/s2.