Question

Find the dimensions of the unknown physical quantity. a,b,c,d .where v=velocity and t=time . V=a+bt+ct²+dt³

Answer 1

As they all adding
So wo suppose thEy all have same dimension as we know only same dimension can be added or subtracted
So v = a ----> 1
V= bt. -----> 2
V= ct2 ----> 3
V= dt3 -----> 4
Solving 1
V = a
L/T = A

SOLVING 2
V =BT
L/T = BT
L/T ÷ T = B
SO
B = L/ T2

SOLVING 3

V = CT2
L/T = C T2
L/T ÷ T2 = C
C = L/T3

SOLVING 4

V =DT3
L/T = D T3
L/T ÷ T3 = D
D = L /T4


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