Q: A projectile is launched horizontally from a cliff with a speed of 15 m/s. If the cliff is 45 m high, how long does it take to hit the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 45}{9.8}} \approx 3.03\ \mathrm{s}$$

Q: A block of mass 5 kg is pulled across a horizontal surface with a constant force of 20 N. If the coefficient of kinetic friction is 0.2, what is the acceleration of the block? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$a = \frac{F - \mu_k mg}{m} = \frac{20 - 0.2 \times 5 \times 9.8}{5} = \frac{20 - 9.8}{5} = 2.04\ \mathrm{m/s^2$}$$

Q: A student throws a ball straight up with an initial velocity of 12 m/s. What is the maximum height reached by the ball? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v^2$}{2g} = \frac{12^2$}{2 \times 9.8} = \frac{144}{19.6} \approx 7.35\ \mathrm{m}$$

Q: A 10 kg box is at rest on a frictionless incline of 30°. What is the magnitude of the force parallel to the incline acting on the box?

$$F = mg \sin \theta = 10 \times 9.8 \times \sin 30^\circ = 98 \times 0.5 = 49\ \mathrm{N}$$

Question 1

A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the car's acceleration?

Accepted Answer

$$a = \frac{20}{10} = 2\ \mathrm{m/s^2$}$$

Question 2

Which of the following best describes Newton's First Law of Motion?

Accepted Answer

An object in motion will remain in motion unless acted upon by an external force.

Question 3

A projectile is launched horizontally from a cliff with a speed of 15 m/s. If the cliff is 45 m high, how long does it take to hit the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 45}{9.8}} \approx 3.03\ \mathrm{s}$$

Question 4

Which of the following is a correct application of the principle of conservation of linear momentum?

Accepted Answer

In a collision between two ice skaters, the total momentum before the collision equals the total momentum after the collision, provided no external forces act.

Question 5

A block of mass 5 kg is pulled across a horizontal surface with a constant force of 20 N. If the coefficient of kinetic friction is 0.2, what is the acceleration of the block? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{F - \mu_k mg}{m} = \frac{20 - 0.2 	imes 5 	imes 9.8}{5} = \frac{20 - 9.8}{5} = 2.04\ \mathrm{m/s^2$}$$

Question 6

Which graph best represents the velocity vs. time for an object experiencing constant acceleration?

Accepted Answer

A straight line with a constant slope.

Question 7

A 2 kg object moving at 3 m/s collides elastically with a stationary 1 kg object. What is the velocity of the 2 kg object after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{2 - 1}{2 + 1} 	imes 3 = \frac{1}{3} 	imes 3 = 1\ \mathrm{m/s}$$

Question 8

A student throws a ball straight up with an initial velocity of 12 m/s. What is the maximum height reached by the ball? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{12^2$}{2 	imes 9.8} = \frac{144}{19.6} \approx 7.35\ \mathrm{m}$$

Question 9

Which statement best describes the principle of superposition as applied to vectors in physics?

Accepted Answer

The resultant vector is the sum of all individual vectors acting on a point.

Question 10

A 10 kg box is at rest on a frictionless incline of 30°. What is the magnitude of the force parallel to the incline acting on the box?

Accepted Answer

$$F = mg \sin 	heta = 10 	imes 9.8 	imes \sin 30^\circ = 98 	imes 0.5 = 49\ \mathrm{N}$$

Question 11

A spinning disk has an angular velocity of $$\omega = 5\ \mathrm{rad/s}$$ and a radius of 0.2 m. What is the linear velocity at the edge of the disk?

Accepted Answer

$$v = \omega r = 5 	imes 0.2 = 1\ \mathrm{m/s}$$

Question 12

A student analyzes a motion graph and observes that the slope of the position vs. time graph is constant. What does this indicate about the object's motion?

Accepted Answer

The object is moving with constant velocity.

Question 13

A 3 kg object is dropped from a height of 8 m. What is its velocity just before hitting the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 8} = \sqrt{156.8} \approx 12.52\ \mathrm{m/s}$$

Question 14

Which of the following is NOT a requirement for equilibrium in a physical system?

Accepted Answer

All forces must act at the center of mass.

Question 15

A 4 kg object moving at 5 m/s collides inelastically with a 2 kg object at rest. What is their final velocity after the collision?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{4 	imes 5 + 2 	imes 0}{4 + 2} = \frac{20}{6} \approx 3.33\ \mathrm{m/s}$$

Question 16

Which of the following best describes the role of free body diagrams in solving physics problems?

Accepted Answer

They help visualize all the forces acting on an object, making it easier to apply Newton's laws.

Question 17

A student pushes a 6 kg box with a force of 30 N on a rough surface. If the box moves at constant velocity, what is the coefficient of kinetic friction? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\mu_k = \frac{F}{mg} = \frac{30}{6 	imes 9.8} = \frac{30}{58.8} \approx 0.51$$

Question 18

A 0.5 kg ball is swung in a horizontal circle of radius 2 m at a speed of 4 m/s. What is the centripetal force acting on the ball?

Accepted Answer

$$F_c = \frac{mv^2$}{r} = \frac{0.5 	imes 4^2$}{2} = \frac{0.5 	imes 16}{2} = \frac{8}{2} = 4\ \mathrm{N}$$

College Physics I: Syllabus and Course Overview

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