Question

Consider the equation s=s0+v0t+a0t2/2+j0t3/6+S0t4/24+ct5/120, where s is a length and t is a time

What are the dimensions and SI units of s0?

a) [L]
b) [L/T]
c) [L/T²]
d) [L/T³]

Answer 1

The dimensions of s0 in the equation s = s0 + v0t + a0t²/2 + j0t³/6 + S0t⁴/24 + ct⁵/120 are [L].

Step-by-step explanation:

The equation provided is s = s0 + v0t + a0t²/2 + j0t³/6 + S0t⁴/24 + ct⁵/120, where s is a length and t is a time. The term s0 represents an initial displacement.

Since the equation is dimensionally consistent, we can determine the dimensions of s0 by comparing the dimensions on both sides of the equation.

From the dimensions given, [s] = L and [t] = T. Since s0 appears alone, its dimensions must be [L]. Therefore, the answer is a) [L].