Question

The distance covered by a particle in time t is given by x = a + bt + ct² + dt³;find the dimensions of a, b, c and d.

Concept of Physics - 1 , HC VERMA , Chapter "Introduction to Physics".

Answer 1

Hello Dear.

Given Equation ⇒
x = a + bt + ct² + dt³

∵ The given equation have Five different terms namely x, a, b, c, d and t.
All of the Terms must have the same dimension of length to give the final dimension([x]) in length.


∴ [x] = L  

 Also, [bt] = L
⇒ b = L/T
⇒ b = LT⁻¹

 Also,  [ct²] = L
⇒ c = L/T²
⇒ c = LT⁻²

  Also, [dt³] = L
⇒ d = L/T³
⇒ d = LT⁻³


[Note → Dimension of x = L & Dimension of t = T]


Hope it helps.

Answer 2

Answer:

Here is your answer........