Question

v=at+b/t+c+v0 is a dimensionally valid equation. obtain the dimesional formula for a,b and c where v is velocity, t is time and v0 is initial velocity.​

Answer 1

Answer:

v is not a dimension less quantity.

V=M^0 L^1 T^-1

then as per the properties of units and dimensions.

In an eqation only the quantities with same dimensions can be added subsctracted.

So.

at has a same dimension as that of b

t+c

c=T^1

now

[v]=[at/t]=[b/t]

M^0 L^1 T^-1 = a T/T

a=[L T^-1]

b=[L]

Answer 2

Answer:

v is not a dimension less quantity.

V=M^0 L^1 T^-1

then as per the properties of units and dimensions.

In an eqation only the quantities with same dimensions can be added subsctracted.

So.

at has a same dimension as that of b

t+c

c=T^1

now

[v]=[at/t]=[b/t]

M^0 L^1 T^-1 = a T/T

a=[L T^-1]

b=[L]