USE UNITS all thru your answer ... don't just append them onto the final number !

Put symbols on a sketch, as you read . . . use meaningful phrases : "v_match" , "catch" , "ground" "turn-around"
. . . show process spans as brackets or vector arrows , with words like   "average" , "losing" , "gaining" , "t=0→2" ...

Write statements as symbols first ... each statement has a SUBJECT ... manipulate symbols before plugging numbers.
. . . keep track of adjectives such as   "initial" , "average" , "final" , "stopped" . . . "change"

subscripts for "total" or "system" , "part A" ...

keep track of the SOURCE for the external Forces applied to the (passive) object

Recognize whether you are predicting based on theory . . . reasoning from causes to their effects ... (what should it do?)
      or whether you are deducing from observation . . . (what does this imply about it?)

Get un-stuck (often) by wondering "why isn't it the same as it used to be?"

it's the Sum of external Forces that cause an object's mass to accelerate subscripts for "total" or "system" , "part A" ...

Topic 4 Summary :

While the Sum of Forces causes the (single) acceleration of an object,
      each individual source of Force is caused by conditions specific to that type of Force .
It turns out that the location of the object , relative to the source , is a key aspect for all types of Force .
. . . features which determine the strength and direction of a Force can be written as a function !

spring Force : depends on the stiffness konstant k of the spring , a scalar property which is intrinsic to a particular spring
      . . . (although a real spring's stiffness does change with age or abuse)
. . . and also depends on the distance and direction which that end of the spring has been stretched : s .
      the spring's end pulls in the opposite direction from its stretch vector (or pushes opposite its compression vector)
      . . . this is parallel to the length of any coil spring.     neglect the mass of ideal (textbook) springs
=> F_spring = − k s .

Two springs hooked end-to-end in series (anchor...spring1...spring2...Force , as : |-v^v^v-·-^v^v^v→ )
      will stretch farther than either one ...the stretch distances add , so s_total = s₁ + s₂ ; their Tensions are the same
=> 1 / k_series = 1 / k₁ + 1 / k₂ .
this implies that longer springs are less stiff   (their k are lower) than otherwise similar short springs .

If two springs are both connected to the anchor and to the external Force, in parallel, ( |‾‾‾→ ) , their Forces add
. . . their stretch distance is the same, but Forces add :
=> k_parallel = k₁ + k₂ .
      this implies that thicker wire springs have larger stiffness k than otherwise similar thin-wire springs .

elastic modulus : even straight steel wire stretches a little bit if pulled with enough Tension ...
. . . the cause of the stretch is stress : Tension spread across the cross-sectional wire Area , in [N/m²] or [N/atom²]
      the effect of stress is strain : fractional length increase , ΔL /L ; the atom-to-atom distance is increased , along T .
. . . the ratio : stress/strain is Young's modulus Y , which is a property of the material (not just the object)
      Y describes the Pressure that would cause its length to double (if it didn't break first)
=> P = Y ΔL/L , for Pressure in solids .
      each atom's bond to its neighbor atom acts essentially like a Hooke's Law spring !

for fluids, which have no intrisic shape, we describe the change in Volume as they are compressed :
. . . each atom itself is a little bit compressible , with non-infinite elastic stiffness .
=> P = −B ΔV/V , where B is called the Bulk Modulus for the material.
      if there were no diagonal bonds in a material, then it's easy to show that B ≈ 3 Y .

Pressure : more intense Pressure at deeper depths within a non-accelerating fluid ;
. . . ΣF_z=m a_z = 0 => P_bottom·A_up = P_top·A_down + m_fluidg ;   m = ρ A×δh
      Pressure at bottom of fluid sample = Pressure at top of fluid sample + ρ g δh ...
=> δP = ρ g δh .

Pressure Units are [N/m²] ; this set of units is also called a "Pascal" , abbreviated Pa .
. . . but other pressure units are also used : besides the "psi" = pound-Force per square inch , there are also
      torr : pressure caused by 1[mm] deep mercury column in standard Earth gravity (9.81[N/kg) . . . and
      "inches of water" , P caused by 1" deep column of water in 9.81[N/kg] gravity . . . and
      "atmosphere" , the pressure caused by "standard" depth (to "sea level") dry Earth atmosphere in standard Earth gravity

. . . Force difference : F_{on bottom} − F_{on top} is called "Buoyant Force" by the fluid on object ;
=> δF = − ρ_fluid g V_object . . . upward ... it used to cancel the weight of fluid that isn't there anymore ... (displaced fluid)
      typical Bouyant Force for condensed matter (solid or liquid) immersed in sparse matter (gas, plasma) is −.001 × mg ;
      but condensed matter can float in other condensed matter ; and some gases float in other gases .
=> for many situations bouyant Forces can NOT be ignored .

Important statement #5 about how the Universe works:

Gravity : every mass in the universe pulls on every other mass in the universe

each source mass M_s contributes to the gravity field g at each location.
. . . the total gravitational influence emanating from source mass M_s ~ GM_s , pointed toward the source mass ,
      with G = 6.67E−11[Nm²/kg²] = 66.7[N/kg · (Mkm)²/(1E30kg)] ,
      or . . . G = 5.931E−3[N/kg · (au)²/M_Solar] <= astronomical units
. . . this influence spreads out, 2 ways in 3-d space, so the contribution to g is weaker far from the source ;
      so strength contributed goes as 1/"distance squared" = 1/r² from that source
      . . . { its contributed g piercing thru the whole surface of any surrounding shell is the same => g·A = 4π GM_s }
=> g_{by M} = G M / r²_M-to-point (toward M) . . . then use   F_{gravity, on m} = mg ;       NOTICE : m ≠ M !

The contribution to g from every source mass (reasonably massive , and reasonably nearby) must be added as a vector
      to get the total   g   at that place (the field point) .
. . . there is only ONE gravity field vector at any location , after adding all the contributions ... (3 components, one vector)

Since the gravitational influence spreads with distance from the souce Mass ,
      the gravity field is more intense on the "near side" of an object than it is on the "far side" of the object.
. . . relative to the average field at the object , these "excess" and "deficit" Forces (per unit object mass) pull outward
      Tidal Tension (per unit mass in the object) = g_near − g_average   and   g_average − g_near   .
=> δg = g / (1 ± Δr/R)²
. . . if the stressed object is small (compared with source Mass distance), this is almost the same on each side , and
=> δg ≈ ( ^d/_dr{g(r)}|_R ) · Δr   . . . ≈ 2gΔr/R   .

For any "field point" inside a hollow spherical shell of mass, the gravity field contributions from the shell Mass will cancel !
. . . only M located non-isotropically around the field point contribute to g .
=> gravity is weaker at the bottom of a deep hole into Earth ... only the "interior" Mass counts .

For any "field point" outside a shell of mass, the gravity field contributions from the shell's Mass will add up to . . .
      exactly the same as if all that Mass was at the center of the shell. (this is a nasty integration, using 3-d vectors)
. . . gravity can't distinguish between a dense Earth center , and a hollow Earth (with very dense shell outside the hollow)