Механика и простые механизмы · AP Physics 1 Unit 1 (Kinematics)
Симулятор графиков скорости v-t и кинематики
Симулятор графиков зависимости скорости от времени (v-t) и кинематики движения
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- Вывод формул
- Режим проектора
- Печатный лист A4
Окно 3D симуляции● 60 FPS
Параметры эксперимента
m/s
m/s²
s
Hz
Расчёты и показатели в реальном времени
Конечная скорость vt
--
Перемещение s
--
Средняя скорость
--
Шаг Δx
--
Вывод формул в реальном времени
Основная формула:
--Подстановка значений:
--Физическое состояние: --
Разбор типовых задач и анализ экзаменационных ошибок
Worked Problem
Условие задачи: A car moving at 15m/s brakes with deceleration 3m/s². Find displacement in 2s and 6s.
Пошаговый вывод формул:
- 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
Условие задачи: Ticker timer with t=0.1s gives x1=2.0cm, x2=2.8cm, x3=3.6cm. Calculate acceleration.
Пошаговый вывод формул:
- Difference Δx = 0.8cm = 0.008m. Acceleration a = Δx / t² = 0.008 / 0.01 = 0.8 m/s².
Рабочий лист для урока и домашние задания
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.
Часто задаваемые вопросы и типичные заблуждения
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.