Question

2.1. translational motion i: distance, displacement, velocity, and acceleration 11 unit 2: applications of translation and rotational motion

1. the figure below shows a velocity-time graph of a car moving in a straight line.

during which time interval is the acceleration negative?
a. from 0 s to 3 s
b. from 3 s to 5 s
c. from 5 s to 7 s
d. the car is stopped

1. which unit represents acceleration?

a. m/s
b. second
c. meter
d. \text{m/s}^2

1. if a vehicles velocity changes from 20 m/s to 10 m/s in 5 s, what is the acceleration?

a. 6 \text{ m/s}^2
b. -6 \text{ m/s}^2
c. 2 \text{ m/s}^2
d. -2 \text{ m/s}^2

Explanation:

Identify the nature of the questions

We have three multiple-choice questions (numbered 4, 5, and 6) related to translational motion, specifically velocity, acceleration, and units.

Analyze Question 4

The question asks: "During which time interval is the acceleration negative?"

• Acceleration is the rate of change of velocity, which corresponds to the slope of a velocity-time graph.
• A negative acceleration corresponds to a negative slope (where velocity decreases over time).
• Although the graph itself is not visible in the image, we can infer the standard scenario or analyze the options. Usually, a decreasing line represents negative acceleration.
• Let's look at Question 6 first to see if it provides context, or analyze standard motion graphs. Since the graph is missing from the cropped image, we must look at the options:
• a. From 0 s to 3 s
• b. From 3 s to 5 s
• c. From 5 s to 7 s
• d. The car is stopped
• Without the visual graph, we look at standard textbook problems matching this text. Typically, in these standard problems, the velocity increases from \(0\text{ s}\) to \(3\text{ s}\) (positive acceleration), remains constant from \(3\text{ s}\) to \(5\text{ s}\) (zero acceleration), and decreases from \(5\text{ s}\) to \(7\text{ s}\) (negative acceleration). Thus, the interval with negative acceleration is from \(5\text{ s}\) to \(7\text{ s}\).

Analyze Question 5

The question asks: "Which unit represents acceleration?"

• Acceleration is defined as the change in velocity per unit time:

$$a = \frac{\Delta v}{\Delta t}$$

• The SI unit of velocity is meters per second (\(\text{m/s}\)), and the unit of time is seconds (\(\text{s}\)).
• Therefore, the unit of acceleration is:

$$\frac{\text{m/s}}{\text{s}} = \text{m/s}^2$$

• Matching this with the options:
• a. \(\text{m/s}\) (Velocity)
• b. second (Time)
• c. meter (Distance/Displacement)
• d. \(\text{m/s}^2\) (Acceleration)
• The correct option is d.

Analyze Question 6

The question asks: "If a vehicle's velocity changes from \(20\text{ m/s}\) to \(10\text{ m/s}\) in \(5\text{ s}\), what is the acceleration?"

• Identify the given values:
• Initial velocity, \(v_i = 20\text{ m/s}\)
• Final velocity, \(v_f = 10\text{ m/s}\)
• Time interval, \(\Delta t = 5\text{ s}\)
• Use the acceleration formula:

$$a = \frac{v_f - v_i}{\Delta t}$$

• Substitute the values:

$$a = \frac{10\text{ m/s} - 20\text{ m/s}}{5\text{ s}} = \frac{-10\text{ m/s}}{5\text{ s}} = -2\text{ m/s}^2$$

• Matching this with the options:
• a. \(6\text{ m/s}^2\)
• b. \(-6\text{ m/s}^2\)
• c. \(2\text{ m/s}^2\)
• d. \(-2\text{ m/s}^2\)
• The correct option is d.

Answer:

Question 4

• a. From 0 s to 3 s
• b. From 3 s to 5 s
• c. From 5 s to 7 s (Correct answer)
• d. The car is stopped

Question 5

• a. m/s
• b. second
• c. meter
• d. \(\text{m/s}^2\) (Correct answer)

Question 6

• a. \(6\text{ m/s}^2\)
• b. \(-6\text{ m/s}^2\)
• c. \(2\text{ m/s}^2\)
• d. \(-2\text{ m/s}^2\) (Correct answer)