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3. Waves, Light & Sound

Wave properties, reflection, refraction, lenses, and electromagnetic spectrum. • All worked solutions and examiner mark schemes are 100% unlocked.

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0625/41/M/J/23 Q1(a)easy[3 Marks]

Uniform Acceleration from Rest

A high-speed train accelerates uniformly from rest to a velocity of 45 m/s in a time of 15 seconds. Calculate the acceleration of the train and state the correct S.I. unit.

u = 0\text{ m/s}, \quad v = 45\text{ m/s}, \quad t = 15\text{ s}

0625/42/O/N/22 Q2(b)medium[4 Marks]

Distance Travelled Under Constant Braking

A car traveling along a horizontal test track at 28 m/s applies its brakes, causing a constant deceleration of 3.5 m/s² until it comes to a complete standstill. Calculate the braking distance required.

u = 28\text{ m/s}, \quad v = 0\text{ m/s}, \quad a = -3.5\text{ m/s}^2

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0625/43/M/J/21 Q3(c)hard[5 Marks]

Terminal Velocity & Non-Linear Air Resistance

A skydiver of total mass 75 kg jumps from an aircraft. At time t = 0, she is falling at 40 m/s, where air resistance opposes her motion with a drag force of 450 N. (i) Calculate her initial downward acceleration at this instant (g = 9.8 m/s²). (ii) Explain why her acceleration decreases to zero as velocity continues to increase.

m = 75\text{ kg}, \quad F_{\text{drag}} = 450\text{ N}, \quad g = 9.8\text{ m/s}^2

0580/42/M/J/23 Q2(a)medium[4 Marks]

Solving Quadratic Equations via Formula

Solve the equation 3x² + 8x - 5 = 0. Give your answers correct to 2 decimal places. Show all your working clearly.

3x^2 + 8x - 5 = 0

0580/43/O/N/22 Q6hard[5 Marks]

Stationary Points & Nature of Turning Points

A curve has equation y = 2x³ - 9x² + 12x - 4. (a) Find dy/dx. (b) Find the coordinates of the two stationary points. (c) Determine the nature of each stationary point using the second derivative.