Question

7. The distance covered by a particle in time t is given by
x = a + bt + ct? + dt; find the dimensions of a, b, c and d.​

Answer 1

Answer:

a has dimensions of distance

b has dimensions of x/t

ct also has x/t

dt also has the same

Answer 2

Given that,

x = a+bt+ct²+dt³

x is the displacement.

Now, by principle of homogeneity

a=bt=ct²=dt³=x

Now, a = L

  [bt]=[L]

 b=[LT−1]

c=[LT−2]

d=[LT−3]

Hence, the dimension of a, b, c and d is [L],[LT−1],[LT−2]and[LT−3]