A rocket accelerates vertically from rest with constant acceleration a. After reaching height h, its acceleration instantaneously changes to -a. What is the maximum height the rocket reaches above its starting point?

A projectile is launched with an initial velocity of 50 m/s at an angle of 30° above the horizontal. If air resistance is negligible, at what time after launch will the horizontal and vertical components of velocity be equal in magnitude?

A rocket's velocity as a function of time is given by v(t) = 20t - 5t², where v is in m/s and t is in seconds. During what time interval is the average acceleration of the rocket zero?

What is the relationship between acceleration and velocity?

How is displacement $$\Delta x$$ calculated in a straight line motion?

A particle is located at a distance r from the center of a uniform sphere of radius R and mass M, where r < R. If the density of the sphere suddenly doubles while its radius remains constant, by what factor does the gravitational force on the particle change?

A block slides down a frictionless incline and then across a rough horizontal surface. If the block-surfaces system is isolated from the environment except for thermal interactions, which physical quantity is conserved within this system?

A particle of mass m moves in a vertical circle at the end of a string of length L. At the lowest point of the circle, which coordinate system would most simplify the analysis of the tension in the string?

Two ice skaters push off each other. What is true about the forces they exert?

A 4.0 kg object and a 6.0 kg object are connected by a light rigid rod of length 2.0 m. If the system rotates about its center of mass with an angular velocity of 3.0 rad/s, what is the total kinetic energy of the system?

In a roller coaster problem, why might zero potential energy be defined at the lowest track point?

A spring with spring constant k = 200 N/m is compressed 0.15 m from its equilibrium position and then released. What is the work done by the spring force as the spring returns to its equilibrium position?

A 4.0 kg object and an 8.0 kg object have the same momentum. What is the ratio of the kinetic energy of the 4.0 kg object to the kinetic energy of the 8.0 kg object?

If a constant force is applied over a displacement, how is work calculated?

In analyzing a complex multi-spring system, a physicist chooses to define the zero of potential energy where the net force on a mass is zero. What is the mathematical significance of this choice?

A 4.0 kg firecracker at rest explodes into three fragments. Two fragments of mass 1.0 kg each travel perpendicular to each other with speeds of 30 m/s and 40 m/s respectively. What is the speed of the third fragment?

Which of the following best describes impulse?

In a closed system with no external forces, what happens if one object gains momentum?

A system consists of a 2 kg block connected to a 3 kg block by a compressed spring. The spring is released, separating the blocks. If we redefine the system to include only the 2 kg block, what physical quantity must be considered to account for the change in the block's momentum?

Two objects, A and B, with masses of 2 kg and 3 kg respectively, collide inelastically on a frictionless surface. Before the collision, object A is moving at 5 m/s towards object B, which is initially at rest. After the collision, the two objects stick together and move with a common velocity. Calculate the total kinetic energy lost during the collision.

Which formula represents the total rotational inertia of multiple objects about an axis?

A rigid triangular plate rotates in a plane about an axis perpendicular to the plate through one vertex. The angular displacement is π/3 radians. Which statement is correct about the linear displacements of points on the plate?

A solid disk of radius R rotates with an angular acceleration α about its central axis. At a particular instant, a point at distance r = R/2 from the center has a tangential acceleration of 3 m/s². What is the tangential acceleration of a point at the rim of the disk at this same instant?

A flywheel with moment of inertia 4.0 kg·m² has an initial angular velocity of 10 rad/s. If it experiences an angular deceleration of -2.0 rad/s², how long will it take for the flywheel to come to a complete stop?

A uniform rod of length L and mass M is pivoted at one end and held horizontally. When released, what is the relationship between its rotational and translational equilibrium states during the subsequent motion?

Develop code used to traverse the elements in a 1D array and determine the result of these traversals.

Represent patterns and algorithms that involve selection and repetition found in everyday life using written language or diagrams.

Develop code to represent nested iterative processes and determine the result of these processes.

All of the following statements regarding the above while loop are true except:

In a quality control simulation, production stops when a specific cutoff is met. What is the printed value of 'passed' when the loop terminates?

If a, b, and c are integers, which of the following conditions is sufficient to guarantee that the expression (a * b < 0) || (a < c && b < c) evaluates to false?

What potential concurrency issue exists in the code above?

Consider the boolean expression: (X && !Y) || (!X && Y). Which of the following best describes when this expression is true?

Which of the following is an example of correctly using if-else where the else block does not require a condition?

All of the following statements about the if-else-if structure in the above code snippet are true except:

What is the output of the program?

Develop code to read input.

Develop code to declare variables of the correct types to hold object references.

Develop code to declare variables to store numbers and Boolean values.

What will be printed when the program is executed?

What is the printed output of ShallowCopyTest?

Which of the following correctly declares and initializes a boolean variable to true?

$$\displaystyle \lim_{x \to 0} \frac{\tan(4x) - \sin(4x)}{x^3}$$ is

Without using a calculator, determine which equation represents a function that approaches $$2$$ as $$x \to 0$$, given the limit property $$\lim_{x\to0} \frac{\sin(2*x)}{x} = 2$$.

$$\displaystyle \lim_{x \to -\infty} \displaystyle\frac{4 \cdot 3^x + 6^x}{2 \cdot 3^x - 1}$$ is

All of the following statements about the Intermediate Value Theorem (IVT) are true EXCEPT:

What are the equations of the horizontal asymptotes of the graph of $$y = \displaystyle\frac{5x^2 + 2}{x^2 + 1}$$?

The function f(x) = $$\frac{x^3-8}{x-2}$$ is graphed above and has a removable discontinuity at x = 2. Compute $$\lim_{x \to 2} f(x)$$.

Evaluate $$\displaystyle\lim\limits_{x \to 2} \frac{|x - 2|}{x^2 - 4}$$. Which of the following best describes the limit?

Without using a calculator, determine which equation represents a continuous, linear function that passes through the points $$(0,2)$$ and $$(4,0)$$.

The function $$\displaystyle h(x) = \frac{x^2 - 9}{x^2 - 2x - 3}$$ has a discontinuity at $$\displaystyle x = 3$$. Which of the following best describes the behavior of $$\displaystyle h$$ at this discontinuity?

Given the table below which shows values of the function $$f(x)=2*x^2+5$$ for values of $$x$$ near 3, determine $$\lim_{x \to 3} f(x)$$.

The function $$ k $$ is continuous on its domain and has vertical asymptote $$ x = -3 $$ and horizontal asymptote $$ y = 7 $$. If $$ \lim_{x \to -3^+} k(x) = +\infty $$ and $$ \lim_{x \to -\infty} k(x) = 7 $$, which of the following statements must be true?

Evaluate $$\lim_{x \to 0} \frac{\sin(x)}{2*x}$$.

Let $$k$$ be the function defined above. Which of the following statements about $$k$$ is true?

Solve the equation: $$\lim_{x\to0}\frac{\cos(x)-1}{x}$$.

Let $$g$$ be the function defined above. Which of the following statements about $$g$$ is true?

Without using a calculator, determine which equation represents a continuous, linear function that passes through the points $$(0,2)$$ and $$(4,0)$$.

How many vertical asymptotes does the graph of $$y = \displaystyle \frac{x^2 - 4}{x^2 + 4}$$ have?

Using the provided graph of f(x) = $$\frac{1}{(x-3)}$$, evaluate $$\lim_{x \to 3^+} \frac{1}{(x-3)}$$.

$$\displaystyle \lim_{x \to \infty} \frac{7e^x + 4x}{2e^x - 5}$$ is

Evaluate $$\lim_{x\to 2} \frac{(x-2)\sqrt{2*x+3}+\left(\frac{1}{x+2}-\frac{1}{4}\right)}{(x-2)\left(\sqrt{x+5}-\sqrt{7}\right)}$$.

What is the value of $$\displaystyle\lim_{x \to \infty} \frac{7x^3 + x^2\cos(x)}{2x^3 + 5x}$$?

Rank the steps in the correct order to evaluate a composite function limit $$\lim_{x\to2} f(g(x))$$, given that $$g(x)$$ is continuous and $$f(x)$$ has a removable discontinuity at the corresponding output value.

What is the value of $$\displaystyle\lim_{x \to \infty} \frac{5x^2 - x^3}{2x^3 + 4x^2}$$?

All of the following statements regarding the limit $$\lim_{x\to3} \frac{x^2-9}{x-3}$$ are true EXCEPT:

$$\lim_{x\to\infty}\frac{5x^3+2}{\sqrt{9x^6+4x^2}}$$ is

Solve the equation: $$\lim_{t\to5}\frac{t^2-t-20}{t-5}$$.

$$\displaystyle\lim_{x \to 0} \dfrac{e^x - 1}{x}$$ is

Evaluate $$\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^{x}$$.

Evaluate $$\displaystyle\lim\limits_{x \to 6} \frac{|x^2 - 36|}{|x - 6|}$$. Which of the following best describes the limit?

Evaluate the limit $$\lim_{x\to 5} (2*x+3)$$.