Deriving the 4th equation of motion

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SUMMARY

The discussion focuses on deriving the fourth equation of motion, expressed as v² = v₀² + 2aD, using the second equation (t = (v - v₀)/a) and the third equation (D = 1/2at² + v₀t). The user successfully substitutes the expression for time into the distance equation to eliminate time, leading to the equation D = 1/2a((v - v₀)/a)² + v₀((v - v₀)/a). The user initially faced challenges with the distribution of terms but ultimately resolved the issue independently.

PREREQUISITES
  • Understanding of kinematic equations in physics
  • Familiarity with algebraic manipulation and distribution of terms
  • Knowledge of variables: initial velocity (v₀), final velocity (v), acceleration (a), and distance (D)
  • Basic grasp of quadratic equations
NEXT STEPS
  • Study the derivation of the first three equations of motion
  • Explore applications of kinematic equations in real-world physics problems
  • Learn about the graphical representation of motion and acceleration
  • Investigate the relationship between acceleration, velocity, and time in various contexts
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Students of physics, educators teaching kinematics, and anyone interested in understanding motion equations and their derivations.

danksnaks
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1. All I need to do is derive the 4th equation of motion being v2= v02+2aD from the second (t=(v-v0)/a) and third (D=1/2at2+v0t).
2. In this case D= (Ending-initial distance) V0= Initial Veolocity
3. By having the second equation solved for t I could substitute it in an completely eliminate time and I end up with D=1/2a((v-v0)/a))2+v0((v-v0)/a). Past this point I knwo to distribute the terms, but I have no idea what the correct forms look like because I always ended up with a slight different in the term hooked to 1/2a. Any help here?
 
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