Derive 1-dimensional motion from average acceleration (no calculus)

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SUMMARY

This discussion focuses on deriving the equation for one-dimensional motion using average acceleration without calculus. It establishes that the average velocity during constant acceleration is the mean of the initial and final velocities, leading to the formula for displacement: x = x0 + v0 t + 1/2 a t². Key variables include initial velocity (v0), final velocity (v1), and constant acceleration (a). The relationship between these variables is crucial for understanding motion in physics.

PREREQUISITES
  • Understanding of average acceleration and its formula (Change in Velocity over Change in Time)
  • Familiarity with basic algebraic manipulation
  • Knowledge of kinematic equations for motion
  • Ability to interpret velocity vs. time graphs
NEXT STEPS
  • Study the derivation of kinematic equations in physics
  • Learn about graphing velocity vs. time and calculating areas under the curve
  • Explore the implications of constant acceleration in real-world scenarios
  • Investigate the relationship between displacement, velocity, and acceleration in different contexts
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the fundamentals of motion and acceleration without the use of calculus.

Gaebril
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Starting with the expressions for average acceleration (Change in Velocity over Change in time), average velocity at constant acceleration; algebraically (NO CALCULUS) derive the equation for one-dimensional motion that relates displacement to the acceleration, assuming acceleration is constant.
 
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Sketch a graph of velocity vs. time and calculate the area under the graph.

s=vt

You can start v0 at any point and vf too.
 
It can be derived based on the fact that with constant acceleration, for any time period, the average velocity during that time period is 1/2 the sum of the initial and final velocity.

v0 = initial velocity
v1 = final velocity
v1 = v0 + at

average velocity = 1/2 (v0 + v1) = 1/2 (v0 + (v0 + at) = v0 + 1/2 a t

distance = initial position + average velocity x time

x = x0 + (v0 + 1/2 a t) t = x0 + v0 t + 1/2 a t2
 

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