Answer:
See Explanation
Explanation:
Given
![s=s_0+v_0t+\frac{a_0t^2}{2}+ \frac{j_0t^3}{6}+\frac{S_0t^4}{24}+\frac{ct^5}{120}](https://tex.z-dn.net/?f=s%3Ds_0%2Bv_0t%2B%5Cfrac%7Ba_0t%5E2%7D%7B2%7D%2B%20%5Cfrac%7Bj_0t%5E3%7D%7B6%7D%2B%5Cfrac%7BS_0t%5E4%7D%7B24%7D%2B%5Cfrac%7Bct%5E5%7D%7B120%7D)
Solving (a): Units and dimension of ![s_0](https://tex.z-dn.net/?f=s_0)
From the question, we understand that:
--- length
--- time
Remove the other terms of the equation, we have:
![s=s_0](https://tex.z-dn.net/?f=s%3Ds_0)
Rewrite as:
![s_0=s](https://tex.z-dn.net/?f=s_0%3Ds)
This implies that
has the same unit and dimension as ![s](https://tex.z-dn.net/?f=s)
Hence:
--- dimension
Length (meters, kilometers, etc.)
Solving (b): Units and dimension of ![v_0](https://tex.z-dn.net/?f=v_0)
Remove the other terms of the equation, we have:
![s=v_0t](https://tex.z-dn.net/?f=s%3Dv_0t)
Rewrite as:
![v_0t = s](https://tex.z-dn.net/?f=v_0t%20%3D%20s)
Make
the subject
![v_0 = \frac{s}{t}](https://tex.z-dn.net/?f=v_0%20%3D%20%5Cfrac%7Bs%7D%7Bt%7D)
Replace s and t with their units
![v_0 = \frac{L}{T}](https://tex.z-dn.net/?f=v_0%20%3D%20%5Cfrac%7BL%7D%7BT%7D)
![v_0 = LT^{-1}](https://tex.z-dn.net/?f=v_0%20%3D%20LT%5E%7B-1%7D)
Hence:
--- dimension
--- unit
Solving (c): Units and dimension of ![a_0](https://tex.z-dn.net/?f=a_0)
Remove the other terms of the equation, we have:
![s=\frac{a_0t^2}{2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7Ba_0t%5E2%7D%7B2%7D)
Rewrite as:
![\frac{a_0t^2}{2} = s_0](https://tex.z-dn.net/?f=%5Cfrac%7Ba_0t%5E2%7D%7B2%7D%20%3D%20s_0)
Make
the subject
![a_0 = \frac{2s_0}{t^2}](https://tex.z-dn.net/?f=a_0%20%3D%20%5Cfrac%7B2s_0%7D%7Bt%5E2%7D)
Replace s and t with their units [ignore all constants]
![a_0 = \frac{L}{T^2}\\](https://tex.z-dn.net/?f=a_0%20%3D%20%5Cfrac%7BL%7D%7BT%5E2%7D%5C%5C)
![a_0 = LT^{-2](https://tex.z-dn.net/?f=a_0%20%3D%20LT%5E%7B-2)
Hence:
--- dimension
--- acceleration
Solving (d): Units and dimension of ![j_0](https://tex.z-dn.net/?f=j_0)
Remove the other terms of the equation, we have:
![s=\frac{j_0t^3}{6}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7Bj_0t%5E3%7D%7B6%7D)
Rewrite as:
![\frac{j_0t^3}{6} = s](https://tex.z-dn.net/?f=%5Cfrac%7Bj_0t%5E3%7D%7B6%7D%20%3D%20s)
Make
the subject
![j_0 = \frac{6s}{t^3}](https://tex.z-dn.net/?f=j_0%20%3D%20%5Cfrac%7B6s%7D%7Bt%5E3%7D)
Replace s and t with their units [Ignore all constants]
![j_0 = \frac{L}{T^3}](https://tex.z-dn.net/?f=j_0%20%3D%20%5Cfrac%7BL%7D%7BT%5E3%7D)
![j_0 = LT^{-3}](https://tex.z-dn.net/?f=j_0%20%3D%20LT%5E%7B-3%7D)
Hence:
--- dimension
--- unit
Solving (e): Units and dimension of ![s_0](https://tex.z-dn.net/?f=s_0)
Remove the other terms of the equation, we have:
![s=\frac{S_0t^4}{24}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7BS_0t%5E4%7D%7B24%7D)
Rewrite as:
![\frac{S_0t^4}{24} = s](https://tex.z-dn.net/?f=%5Cfrac%7BS_0t%5E4%7D%7B24%7D%20%3D%20s)
Make
the subject
![S_0 = \frac{24s}{t^4}](https://tex.z-dn.net/?f=S_0%20%3D%20%5Cfrac%7B24s%7D%7Bt%5E4%7D)
Replace s and t with their units [ignore all constants]
![S_0 = \frac{L}{T^4}](https://tex.z-dn.net/?f=S_0%20%3D%20%5Cfrac%7BL%7D%7BT%5E4%7D)
![S_0 = LT^{-4](https://tex.z-dn.net/?f=S_0%20%3D%20LT%5E%7B-4)
Hence:
--- dimension
--- unit
Solving (e): Units and dimension of ![c](https://tex.z-dn.net/?f=c)
Ignore other terms of the equation, we have:
![s=\frac{ct^5}{120}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7Bct%5E5%7D%7B120%7D)
Rewrite as:
![\frac{ct^5}{120} = s](https://tex.z-dn.net/?f=%5Cfrac%7Bct%5E5%7D%7B120%7D%20%3D%20s)
Make
the subject
![c = \frac{120s}{t^5}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B120s%7D%7Bt%5E5%7D)
Replace s and t with their units [Ignore all constants]
![c = \frac{L}{T^5}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7BL%7D%7BT%5E5%7D)
![c = LT^{-5}](https://tex.z-dn.net/?f=c%20%3D%20LT%5E%7B-5%7D)
Hence:
--- dimension
--- units