Q: A projectile is launched at an angle $$\theta$$ above the horizontal with initial speed $$v_0. $$Neglecting air resistance, what is the time of flight until it returns to the same vertical level?

$$t = \dfrac{2v_0 \sin \theta}{g}$$

Question 1

A car accelerates from rest along a straight road. If its acceleration is given by $$a(t) = 3t ($$where $$a is in$$ $$\mathrm{m/s^2$}$$ and $$t in$$ $$\mathrm{s}$$), what is the car's velocity after 4 seconds?

Accepted Answer

$$v(4) = 24\ \mathrm{m/s}$$

Question 2

Which of the following statements best describes Newton’s Third Law?

Accepted Answer

For every action, there is an equal and opposite reaction, and these forces act on different objects.

Question 3

A projectile is launched at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$Neglecting air resistance, what is the time of flight until it returns to the same vertical level?

Accepted Answer

$$t = \dfrac{2v_0 \sin 	heta}{g}$$

Question 4

A block slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 5

A 2 kg object moving at $$5\ \mathrm{m/s}$$ collides elastically with a stationary 3 kg object. What is the velocity of the 2 kg object after the collision?

Accepted Answer

$$v = -1\ \mathrm{m/s}$$

Question 6

A spinning disk of mass $$M$$ and radius $$R$$ rotates with angular velocity $$\omega. $$What is its angular momentum about its center?

Accepted Answer

$$L = \dfrac{1}{2}MR^2$\omega$$

Question 7

A student measures the length of a rod as $$1.20\ \mathrm{m}$$ with an uncertainty of $$0.02\ \mathrm{m}. $$What is the percent uncertainty?

Accepted Answer

$$1.67\%$$

Question 8

A satellite orbits Earth at a distance $$r$$ from the center. What is the gravitational force acting on it?

Accepted Answer

$$F = \dfrac{GmM}{r^2$}$$

Question 9

A fluid flows through a pipe with varying diameter. According to the continuity equation, what happens to the speed of the fluid as the diameter decreases?

Accepted Answer

The speed increases.

Question 10

A ball is thrown vertically upward with initial velocity $$v_0. $$Using calculus, what is the maximum height reached?

Accepted Answer

$$h = \dfrac{v_0$^2}{2g}$$

Question 11

A 5 kg object is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}. If it is $$pulled and released from rest at $$x = 0.1\ \mathrm{m}$$, what is its maximum speed?

Accepted Answer

$$v_{max} = \sqrt{\dfrac{k x^2$}{m}}$$

Question 12

A uniform rod of length $$L$$ and mass $$M$$ rotates about one end. What is its moment of inertia?

Accepted Answer

$$I = \dfrac{1}{3}ML^2$

Question 13

A student drops a ball from a height $$h. $$Which equation gives the time to reach the ground, neglecting air resistance?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 14

A force $$F is $$applied to a mass $$m$$ for a time $$\Delta t. $$What is the change in momentum?

Accepted Answer

$$\Delta p = F \Delta t$$

Question 15

A student pushes a box across a rough surface at constant speed. Which statement is true about the forces?

Accepted Answer

The applied force is equal to the friction force.

Question 16

A pendulum swings with small amplitude. What is the period of the pendulum?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{L}{g}}$$

Question 17

A student analyzes a collision between two cars using conservation of momentum. Which equation should be used?

Accepted Answer

$$m_1 v$$_{1i} + $$m_2 v$$_{2i} = $$m_1 v$$_{1f} + $$m_2 v$$_{2f}$$

Question 18

A student uses calculus to find the work done by a variable force $$F(x) = 4x$$ from $$x = 0 to$$ $$x = 3\ \mathrm{m}. $$What is the work?

Accepted Answer

$$W = \$$int_0$$^3 4x\ dx = 18\ \mathrm{J}$$

Question 19

A student measures the acceleration of a cart on an incline and finds it to be $$a = 2.5\ \mathrm{m/s^2$}$$ with an uncertainty of $$0.1\ \mathrm{m/s^2$}. $$What is the percent uncertainty?

Accepted Answer

$$4\%$$

PHYS 1100 Course Outline and Study Guide: Calculus-Based Physics 1

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