Position → Velocity → Acceleration: f(x) = x², f'(x) = 2x, ∫x² dx = (1/3)x³ + C, Sound wave or circular motion: f(x) = sin(x), f'(x) = cos(x), ∫sin(x) dx = -cos(x) + C, Population growth or compound interest: f(x) = e^x, f'(x) = e^x, ∫e^x dx = e^x + C, Inverse relationships (gravity, light): (x) = 1/x, f'(x) = -1/x², ∫1/x dx = ln|x| + C, Harmonic motion (spring, pendulum): f(x) = cos(x), f'(x) = -sin(x), ∫cos(x) dx = sin(x) + C,

Let's get Real with Maths and PhysicsReal-life Motion Example

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