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Newton’s First Law – Force Needed to Start Motion
At Indira Gandhi International Airport, a heavy suitcase is sitting on a stationary conveyor belt. The belt is initially at rest...

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Newton’s Second Law – Acceleration of a Mars Rover
At NASA's robotics laboratory, engineers are preparing a prototype rover for a future mission to Mars. Before sending the rover...

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Newton’s Second Law – Force Required to Accelerate a Rocket Cart
At ISRO's training center, engineering students are testing a small rocket-powered cart on a straight frictionless track. The ca...

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Given a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.
Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries. Return the total area (A) of...

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5-year Annedversaries
This is the Bonus Round problem for the 2025 Cody Contest. Attend the watch party on Friday, March 27 to see how 6 champions fro...

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Angular Velocity of a Falling Rod Pivoted at One End (Energy + Rotation)
Engineers at Indian Institute of Technology Bombay are designing a rotating docking arm for a future space station. The arm is m...

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Angular Velocity Required to Create Artificial Gravity
Scientists at NASA and Indian Space Research Organisation are designing a rotating space station ring to simulate Earth-like gra...

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Moment of Inertia Using Parallel Axis Theorem
Engineers at Indian Space Research Organisation are designing a satellite with extendable robotic arms. When the arms extend out...

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Acceleration in a Symmetric Double-Pulley Constraint System
Engineers at Indian Institute of Technology Kanpur are designing a precision counterweight system for high-speed elevators. The ...

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Tension in String for Circular Motion (Advanced Rotational Dynamics)
At the astronaut training facility of Indian Space Research Organisation, astronauts are trained using a rotating centrifuge. Th...

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Motion of a Bead Sliding on a Rotating Rod (Non-Inertial Frame Dynamics)
Scientists at Indian Space Research Organisation are testing artificial gravity inside a rotating space station module. Inside ...

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Acceleration of Block Relative to Ground
Researchers at Indian Space Research Organisation test cargo motion inside accelerating spacecraft ramps. Find acceleration.

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Acceleration in an Atwood Machine with Massive Pulley
Engineers at Indian Institute of Technology Delhi are designing a precision elevator calibration system using two masses connect...

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Velocity of a Particle Under Constant Acceleration Using Energy Methods
Scientists at CERN are testing a linear accelerator that uses electromagnetic force to accelerate charged particles along a stra...

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Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...

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Rotating 2d curve around a vertical axis
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotatio...

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Rotating the plane region bounded by two polynomials
Let p and q be n-degree and m-degree polynomials with n >= m >= 1. Consider clockwise rotate the plane region bounded by these t...

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Odd Run Sums
Given a row vector x of integers, find every maximal run of consecutive odd numbers and return a row vector containing the sum o...

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Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor
Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k, that vertically transforms ...

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Scaling vertically parabola by evaluating its area over an interval
Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the...

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Scaling vertically functions
Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by...

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Shifting vertically even-degree polynomial's graph by its mean over an interval
Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by...

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Translating even-degree polynomial by its vertex to the origin
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting ...

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Translating parabola by its vertex to the origin
Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the ...

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Shifting vertically a function's graph
Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k. For a ...

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Is it Possible? ( Easy )
In the first part of series, we simplify the problem. Given two jugs with capacities A and B, and a target amount T, determine i...

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Power of Moving Vehicle
Engineers at Tesla calculate how much power is required to maintain vehicle motion.

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Spring Energy Storage
Engineers at Bosch design suspension systems using springs. They calculate the energy stored when the spring compresses.

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Machine Efficiency Test
Engineers at Siemens test how efficiently a motor converts electrical energy into mechanical work.

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