. Consider the equation =0+0+02/2+03/6+04/24+5/120, where s is a length and t is a time. What are the dimensions and SI units of (a) 0, (b) 0, (c) 0, (d) 0, (e) 0, and (f) c?

See Explanation

Explanation:

Given

Solving (a): Units and dimension of

From the question, we understand that:

--- length

--- time

Remove the other terms of the equation, we have:

Rewrite as:

This implies that has the same unit and dimension as

Hence:

--- dimension

Length (meters, kilometers, etc.)

Solving (b): Units and dimension of

Remove the other terms of the equation, we have:

Rewrite as:

Make the subject

Replace s and t with their units

Hence:

--- dimension

--- unit

Solving (c): Units and dimension of

Remove the other terms of the equation, we have:

Rewrite as:

Make the subject

Replace s and t with their units [ignore all constants]

Hence:

--- dimension

--- acceleration

Solving (d): Units and dimension of

Remove the other terms of the equation, we have:

Rewrite as:

Make the subject

Replace s and t with their units [Ignore all constants]

Hence:

--- dimension

--- unit

Solving (e): Units and dimension of

Remove the other terms of the equation, we have:

Rewrite as:

Make the subject

Replace s and t with their units [ignore all constants]

Hence:

--- dimension

--- unit

Solving (e): Units and dimension of

Ignore other terms of the equation, we have:

Rewrite as:

Make the subject

Replace s and t with their units [Ignore all constants]

Hence:

--- dimension

--- units