Mechanics & Simple Machines · AP Physics 1 Unit 1 (Kinematics)
Kinematics Ticker-Tape & v-t Graph Simulator
Key exam takeaway: The slope of a v-t graph represents acceleration; the area under the v-t graph represents displacement.
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3D Simulation Stage● 60 FPS
Parameter Controls
m/s
m/s²
s
Hz
Live Derivations & Metrics
Final Velocity vt
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Displacement s
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Average Velocity
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Interval Difference Δx
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: A car moving at 15m/s brakes with deceleration 3m/s². Find displacement in 2s and 6s.
Step-by-Step Derivation:
- Stopping time t0 = 15/3 = 5s. In 2s: s = 15*2 - 0.5*3*4 = 24m. In 6s: car stopped at 5s, so s = 15²/(2*3) = 37.5m.
Worked Problem
Problem: Ticker timer with t=0.1s gives x1=2.0cm, x2=2.8cm, x3=3.6cm. Calculate acceleration.
Step-by-Step Derivation:
- Difference Δx = 0.8cm = 0.008m. Acceleration a = Δx / t² = 0.008 / 0.01 = 0.8 m/s².
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: In a v-t graph, what do horizontal lines, upward sloped lines, and t-axis intercepts mean?
Answer Key: Horizontal: uniform motion; upward slope: uniform acceleration; t-axis intercept: instantaneous velocity is zero.
Q2. Variant 2: An object covers 2m in 1st second, 4m in 2nd second, 6m in 3rd. Find v0 and a.
Answer Key: Δx = 2m = a(1²) => a = 2 m/s². From s1 = v0(1) + 0.5(2)(1) = 2 => v0 = 1 m/s.
Q3. Variant 3: Car A at 10m/s chases Car B at 4m/s initially 20m ahead. Car A decelerates at 1m/s². Does A catch B?
Answer Key: Velocities equalize at t = (10-4)/1 = 6s. Car A travels 42m; Car B travels 24m. Net gain = 18m < 20m, so A never catches B.
Frequently Asked Questions & Misconceptions
What is the most common confusion between x-t and v-t graphs?
x-t graph slope is velocity, horizontal means rest; v-t graph slope is acceleration, horizontal means uniform motion. Neither represents the spatial trajectory!
Why is car braking considered the classic kinematics pitfall?
Because real cars stop when velocity hits zero rather than reversing. Formulas must not be applied beyond the stopping moment.
What is the advantage of the successive difference method in ticker tape analysis?
It incorporates all measured segment displacements, effectively averaging out random measurement errors.
What is the critical criterion in catch-up problems?
The moment when velocities become equal. If separation remains positive at equal velocity, collision is avoided.