Q: A vector $$ \vec{A} $$ has a magnitude of 10 units and points at an angle of 30° above the x-axis. What is the y-component of $$ \vec{A} $$?

$$A_y = 10 \times \sin(30^\circ)$$

Q: A car moves along a straight road. Its position as a function of time is given by $$x(t) = 4t^2$ + 2t. $$What is the car's velocity at $$t = 3 s$$?

$$v = \frac{dx}{dt} = 8t + 2 = 8 \times 3 + 2 = 26 m/s$$

Q: A 2 kg block is at rest on a horizontal surface. The coefficient of static friction is 0.4. What is the maximum force that can be applied before the block starts to move?

$$F_{max} = 0.4 \times 2 \times 9.8 = 7.84 N$$

Q: A 5 kg object is moving at 10 m/s. What is its momentum?

$$p = 5 \times 10 = 50 kg$$\cdot m/s

Q: A force of 20 N acts on a 4 kg object for 2 seconds. What is the change in momentum (impulse) delivered to the object?

$$\Delta p = 20 \times 2 = 40 kg$$\cdot m/s

Q: A 10 kg box is pulled up a 30° incline with a constant velocity. If the coefficient of kinetic friction is 0.2, what is the friction force acting on the box?

$$f_k = 0.2 \times 10 \times 9.8 \times \cos(30^\circ)$$

Q: A 3 kg object is attached to a string and swung in a horizontal circle of radius 2 m at a speed of 4 m/s. What is the tension in the string?

$$T = \frac{3 \times 4^2$}{2} = 24 N$$

Question 1

A vector $$ \vec{A} $$ has a magnitude of 10 units and points at an angle of 30° above the x-axis. What is the y-component of $$ \vec{A} $$?

Accepted Answer

$$A_y = 10 	imes \sin(30^\circ)$$

Question 2

A car moves along a straight road. Its position as a function of time is given by $$x(t) = 4t^2$ + 2t. $$What is the car's velocity at $$t = 3 s$$?

Accepted Answer

$$v = \frac{dx}{dt} = 8t + 2 = 8 	imes 3 + 2 = 26 m/s$$

Question 3

Which of the following best describes the difference between speed and velocity?

Accepted Answer

Velocity includes direction, speed does not.

Question 4

A ball is thrown horizontally from the top of a 20 m high building with a speed of 5 m/s. How long does it take to hit the ground? (Ignore air resistance, $$g = 9.8 m/s$^2)$$

Accepted Answer

$$t = \sqrt{\frac{20}{9.8}} \approx 1.43 s$$

Question 5

Which force is responsible for keeping a car moving in a circle on a flat road?

Accepted Answer

Friction force

Question 6

A 2 kg block is at rest on a horizontal surface. The coefficient of static friction is 0.4. What is the maximum force that can be applied before the block starts to move?

Accepted Answer

$$F_{max} = 0.4 	imes 2 	imes 9.8 = 7.84 N$$

Question 7

A 5 kg object is moving at 10 m/s. What is its momentum?

Accepted Answer

$$p = 5 	imes 10 = 50 kg$$\cdot m/s

Question 8

A force of 20 N acts on a 4 kg object for 2 seconds. What is the change in momentum (impulse) delivered to the object?

Accepted Answer

$$\Delta p = 20 	imes 2 = 40 kg$$\cdot m/s

Question 9

A 10 kg box is pulled up a 30° incline with a constant velocity. If the coefficient of kinetic friction is 0.2, what is the friction force acting on the box?

Accepted Answer

$$f_k = 0.2 	imes 10 	imes 9.8 	imes \cos(30^\circ)$$

Question 10

Which of the following statements about Newton’s Second Law is correct?

Accepted Answer

It states that force is proportional to acceleration.

Question 11

A 3 kg object is attached to a string and swung in a horizontal circle of radius 2 m at a speed of 4 m/s. What is the tension in the string?

Accepted Answer

$$T = \frac{3 	imes 4^2$}{2} = 24 N$$

Question 12

A motion diagram shows an object moving with increasing spacing between position markers. What does this indicate about the object's motion?

Accepted Answer

The object is accelerating.

Question 13

A velocity vs. time graph for an object shows a straight line with positive slope. What does this indicate?

Accepted Answer

The object is accelerating at a constant rate.

Question 14

A 6 kg object is suspended by a rope. What is the tension in the rope if the object is at rest?

Accepted Answer

$$T = 6 	imes 9.8 = 58.8 N$$

Question 15

A 2 kg object is dropped from rest. What is its velocity after 3 seconds? (Ignore air resistance, $$g = 9.8 m/s$^2)$$

Accepted Answer

$$v = 9.8 	imes 3 = 29.4 m/s$$

Question 16

A 1 kg ball is thrown upward with a velocity of 15 m/s. What is the maximum height it reaches? (Ignore air resistance, $$g = 9.8 m/s$^2)$$

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{15^2$}{2 	imes 9.8} \approx 11.5 m$$

Question 17

A 4 kg object is moving at 8 m/s. It collides with a stationary 2 kg object and they stick together. What is their final velocity?

Accepted Answer

$$v_f = \frac{4 	imes 8}{4 + 2} = 5.33 m/s$$

Question 18

A 7 kg object is pulled by a force of 21 N. What is its acceleration?

Accepted Answer

$$a = \frac{21}{7} = 3$$ $$m/s^2$$

Question 19

A 2 kg object is moving in a circle of radius 1 m at a speed of 3 m/s. What is the centripetal acceleration?

Accepted Answer

$$a_c = \frac{3^2$}{1} = 9$$ $$m/s^2$$

Physics with Calculus: Exam 1 Study Notes – Kinematics, Newtonian Mechanics, and Momentum

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