Q: A car moves from point $$P_1 to$$ $$P_2 in $$the $$x$$-$$y$$ plane. The displacement vector is $$\vec{\Delta r} = (3.0, 4.0)\ \text{m}$$ and the time interval is $$\Delta t = 0.5\ \text{s}. $$What is the magnitude of the average velocity?

$$v_{\text{avg}} = \frac{\sqrt{3.0^2$ + 4.0^2$}}{0.5}$$

Question 1

A soccer ball is kicked from ground level with an initial speed of $$v_0 = 20$$\ 	ext{m/s}$$ at an angle of $$\$$theta_0 = 30$$^\circ$$ above the horizontal. Neglecting air resistance, what is the maximum height reached by the ball?

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ \$$theta_0$$}{2g}$$

Question 2

Which of the following statements about static and kinetic friction is TRUE?

Accepted Answer

Static friction prevents motion up to a maximum value, while kinetic friction acts during motion.

Question 3

A block of mass $$m is $$pulled across a horizontal surface with a constant velocity by a force $$F$$ applied via a rope. If the coefficient of kinetic friction is $$\mu_k$$, what is the magnitude of the applied force?

Accepted Answer

$$F = \mu_k m g$$

Question 4

A projectile is launched from ground level with an initial velocity $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. Which equation gives the total time the projectile is in the air?

Accepted Answer

$$T = \frac{2 v_0$ \sin \$$theta_0$$}{g}$$

Question 5

Which of the following best describes the direction of the instantaneous velocity vector for an object moving along a curved path in the $$x$$-$$y$$ plane?

Accepted Answer

It is always tangent to the object's path.

Question 6

A hockey puck slides on ice with an initial velocity $$v_0$$ and comes to rest after traveling a distance $$d. If $$the coefficient of kinetic friction between the puck and ice is $$\mu_k$$, what is the acceleration of the puck?

Accepted Answer

$$a = -\mu_k g$$

Question 7

A car moves from point $$P_1 to$$ $$P_2 in $$the $$x$$-$$y$$ plane. The displacement vector is $$\vec{\Delta r} = (3.0, 4.0)\ 	ext{m}$$ and the time interval is $$\Delta t = 0.5\ 	ext{s}. $$What is the magnitude of the average velocity?

Accepted Answer

$$v_{	ext{avg}} = \frac{\sqrt{3.0^2$ + 4.0^2$}}{0.5}$$

Question 8

Which of the following is NOT a correct statement about Newton's Laws of Motion?

Accepted Answer

They only apply to objects moving at constant velocity.

Question 9

A child pulls a toy chest with a rope at an angle $$	heta$$ above the horizontal. The normal force $$N$$ exerted by the floor on the chest is given by:

Accepted Answer

$$N = m g - F \sin 	heta$$

Question 10

Which equation correctly gives the range $$R of a $$projectile launched from ground level with initial speed $$v_0 at $$angle $$\$$theta_0$$?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2\$$theta_0$$}{g}$$

Question 11

A block is held against a vertical wall by a horizontal force $$F. If $$the coefficient of static friction is $$\mu_s$$, what is the minimum value of $$F$$ required to prevent the block from sliding down?

Accepted Answer

$$F = \frac{mg}{\mu_s}$$

Question 12

Which of the following best describes the effect of increasing the normal force between two surfaces in contact?

Accepted Answer

It increases the frictional force.

Question 13

A projectile is launched with initial velocity components $$v_{0x}$$ and $$v_{0y}. $$Which equation gives the vertical position $$y(t) at $$time $$t$$?

Accepted Answer

$$y(t) = y_0$ + v_{0y} t - \frac{1}{2} g t^2$

Question 14

Which of the following is a correct statement about the direction of the acceleration vector for an object moving along a curved path?

Accepted Answer

It always points toward the concave side of the curved path.

Question 15

A free-body diagram is useful for:

Accepted Answer

Visualizing the forces acting on a single object or system.

Question 16

A penguin slides down an icy incline of $$10.0^\circ$$ with a mass of $$32.0\ 	ext{kg}. If $$the coefficient of kinetic friction is $$\mu_k = 0.05$$, what is the net force acting on the penguin?

Accepted Answer

$$F_{	ext{net}} = m g \sin 	heta - \mu_k m g \cos 	heta$$

Question 17

Which of the following is the correct expression for the magnitude of the position vector $$\vec{r} in $$two dimensions?

Accepted Answer

$$|\vec{r}| = \sqrt{x^2$ + y^2$}$$

Question 18

Which of the following is a correct statement about the coefficient of friction?

Accepted Answer

It is a dimensionless number that characterizes the interaction between two surfaces.

Study Notes: Two-Dimensional Motion, Friction, and Newton's Laws

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