### Concept Items

### 5.1 Vector Addition and Subtraction: Graphical Methods

There is a vector $\overrightarrow{\text{A}}$, with magnitude 5 units pointing towards west and vector $\overrightarrow{\text{B}}$, with magnitude 3 units, pointing towards south. Using vector addition, calculate the magnitude of the resultant vector.

- 4.0
- 5.8
- 6.3
- 8.0

- By joining the head of the first vector to the head of the last
- By joining the head of the first vector with the tail of the last
- By joining the tail of the first vector to the head of the last
- By joining the tail of the first vector with the tail of the last

- ${110}^{\circ}$
- ${160}^{\circ}$
- ${200}^{\circ}$
- ${290}^{\circ}$

### 5.2 Vector Addition and Subtraction: Analytical Methods

- ${0}^{\circ}$
- ${45}^{\circ}$
- ${90}^{\circ}$
- ${180}^{\circ}$

- The magnitude of the resultant vector will be zero.
- The magnitude of resultant vector will be twice the magnitude of the original vector.
- The magnitude of resultant vector will be same as magnitude of the original vector.
- The magnitude of resultant vector will be half the magnitude of the original vector.

- ${A}_{x}=A\mathrm{cos}\theta $ ${A}_{y}=A\mathrm{sin}\theta $
- ${A}_{x}=A\mathrm{cos}\theta $ ${A}_{y}=A\mathrm{cos}\theta $
- ${A}_{x}=A\mathrm{sin}\theta $ ${A}_{y}=A\mathrm{cos}\theta $
- ${A}_{x}=A\mathrm{sin}\theta $ ${A}_{y}=A\mathrm{sin}\theta $

True or False—Every 2-D vector can be expressed as the product of its x and y-components.

- True
- False

### 5.3 Projectile Motion

- Any object in projectile motion falls at the same rate as an object in freefall, regardless of its horizontal velocity.
- All objects in projectile motion fall at different rates, regardless of their initial horizontal velocities.
- Any object in projectile motion falls at the same rate as its initial vertical velocity, regardless of its initial horizontal velocity.
- All objects in projectile motion fall at different rates and the rate of fall of the object is independent of the initial velocity.

- $-9.8\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $-9.8\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$
- $9.8\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $9.8\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$

### 5.4 Inclined Planes

True or False—Kinetic friction is less than the limiting static friction because once an object is moving, there are fewer points of contact, and the friction is reduced. For this reason, more force is needed to start moving an object than to keep it in motion.

- True
- False

- ${f}_{\text{s}}\le N$
- ${f}_{s}\le {\mu}_{\text{s}}N$
- ${f}_{s}\ge N$
- ${f}_{s}\ge {\mu}_{\text{s}}N$

- ${f}_{\text{k}}={\mu}_{\text{s}}N$
- ${f}_{\text{k}}={\mu}_{\text{k}}N$
- ${f}_{\text{k}}\le {\mu}_{\text{s}}N$
- ${f}_{\text{k}}\le {\mu}_{\text{k}}N$

### 5.5 Simple Harmonic Motion

- The negative sign indicates that displacement decreases with increasing force.
- The negative sign indicates that the direction of the applied force is opposite to that of displacement.
- The negative sign indicates that the direction of the restoring force is opposite to that of displacement.
- The negative sign indicates that the force constant must be negative.

With reference to simple harmonic motion, what is the equilibrium position?

- The position where velocity is the minimum
- The position where the displacement is maximum
- The position where the restoring force is the maximum
- The position where the object rests in the absence of force

- Restoring force is directly proportional to the displacement from the mean position and acts in the the opposite direction of the displacement.
- Restoring force is directly proportional to the displacement from the mean position and acts in the same direction as the displacement.
- Restoring force is directly proportional to the square of the displacement from the mean position and acts in the opposite direction of the displacement.
- Restoring force is directly proportional to the square of the displacement from the mean position and acts in the same direction as the displacement.