Question 1

Which of the following best describes the displacement vector $$\Delta \vec{r}$$ shown in the first two images?

Accepted Answer

It is the difference between the final and initial position vectors: $$\Delta \vec{r} = \vec{r}_f - \vec{r}_i.$$

Question 2

A car moves from position $$\vec{x}_0 to$$ $$\vec{x} as $$shown in the third image. If the elapsed time is $$t - t_0$, what is the formula for the average velocity?

Accepted Answer

$$\displaystyle \frac{\vec{x} - \vec{x}_0}{t - t_0$}$$

Question 3

In the trip from Killarney to Cork (see the vector diagram), what is the correct method to find the total displacement vector?

Accepted Answer

Add the vectors using their components: $$\Delta x = A_x + B_x + C_x$$, $$\Delta y = A_y + B_y + C_y.$$

Question 4

Given $$\Delta x = 38.63\ \mathrm{km}$$ and $$\Delta y = -22.2\ \mathrm{km}$$, what is the magnitude of the displacement vector?

Accepted Answer

$$\sqrt{(38.63)^2$ + (-22.2)^2$}\ \mathrm{km} = 45\ \mathrm{km}$$

Question 5

A butterfly flies from point $$a to$$ $$e$$ along a curved path, but its average velocity is calculated as $$\vec{v}_{av} = \frac{\Delta \vec{r}}{\Delta t}. $$Why is this correct?

Accepted Answer

Average velocity depends only on the straight-line displacement and total time.

Question 6

On a position vs. time graph, what does the slope of the chord between two points represent?

Accepted Answer

The average velocity over the time interval.

Question 7

A car travels $$1609\ \mathrm{m} in$$ $$4.740\ \mathrm{s} in $$one direction and $$-1609\ \mathrm{m} in$$ $$4.695\ \mathrm{s} in $$the opposite direction. What is the average velocity for the first run?

Accepted Answer

$$\displaystyle \frac{1609\ \mathrm{m}}{4.740\ \mathrm{s}} = 339.5\ \mathrm{m/s}$$

Question 8

On a velocity vs. time graph, what does the area under the curve represent?

Accepted Answer

The displacement.

Question 9

A suitcase of mass $$36.0\ \mathrm{kg} is $$pulled with a force of $$65.0\ \mathrm{N} at$$ $$40.0^\circ$$ above the horizontal. What is the normal force acting on the suitcase?

Accepted Answer

$$N = mg - F \sin 40.0^\circ$$

Question 10

A brick slides down a frictionless roof inclined at $$30.0^\circ. $$What is the component of gravitational force parallel to the roof?

Accepted Answer

$$mg \sin 30.0^\circ$$

Question 11

Two blocks, $$m_1 = 26.0$$\ \mathrm{kg}$$ and m_2$ = 42.0\ \mathrm{kg}$$, are connected by a cord over a pulley. What is the acceleration of the system?

Accepted Answer

$$a = \frac{(m_2$ - m_1$)g}{m_1$ + m_2$}$$

Question 12

If a net force $$\sum \vec{F}$$ acts on a mass $$m$$, what is the resulting acceleration?

Accepted Answer

$$\vec{a} = \frac{\sum \vec{F}}{m}$$

Question 13

A train engine pulls five identical freight cars, each weighing $$90.0\ \mathrm{kN}. If $$the train reaches $$15.0\ \mathrm{m/s} in$$ $$5.00\ \mathrm{min}$$, what is the acceleration of the train?

Accepted Answer

$$a = \frac{15.0\ \mathrm{m/s}}{300\ \mathrm{s}} = 0.05\ \mathrm{m/s}^2$$

Question 14

A $$1.0\ \mathrm{kg}$$ brick slides down a $$30.0^\circ$$ frictionless roof for $$0.90\ \mathrm{s}$$ starting from rest. What is its speed at the edge?

Accepted Answer

$$v = g \sin 30.0^\circ 	imes 0.90$$

Question 15

If the net force on an object is zero, what can be said about its velocity?

Accepted Answer

It is constant (could be zero or nonzero).

Question 16

A $$36.0\ \mathrm{kg}$$ suitcase is pulled with a $$65.0\ \mathrm{N}$$ force at $$40.0^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$\mu_k = 0.13$$, what is the frictional force?

Accepted Answer

$$f_k = \mu_k N$$

Question 17

Which of the following statements about mass is correct according to Newton’s second law?

Accepted Answer

Mass is a measure of an object's inertia, or resistance to changes in velocity.

Question 18

A skater slows down from $$8.94\ \mathrm{m/s} to$$ $$7.15\ \mathrm{m/s}$$ while climbing a $$15.0^\circ$$ hill in $$120.0\ \mathrm{s}. $$What is the average acceleration magnitude?

Accepted Answer

$$\displaystyle \frac{\sqrt{(-2.03)^2$ + (1.85)^2$}}{120.0} = 0.0229\ \mathrm{m/s}^2$$

Question 19

If the acceleration and velocity vectors of an object point in opposite directions, what happens to the object?

Accepted Answer

It slows down (decelerates).

Acceleration and Newton’s Second Law: Position, Displacement, Velocity, and Force

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