Question

based on the velocity vs. time graph below, when is the object in dynamic equilibrium?
check all that apply.
graph 1: velocity vs time
v (m/s)
20
10
10 20 30 40 time (s)
☐ 0 to 10 seconds
☐ 10 to 20 seconds
☐ 20 to 30 seconds
☐ 30 to 40 seconds
an object moving horizontally has a velocity of -3.0 m/s. which of the following are true?
check all that apply.
☐ the object is moving left
☐ the object is moving right
☐ the velocity is changing by 3 meters every second
☐ the position is changing by 3 meters every second

Explanation:

First Question (Velocity vs. Time Graph - Dynamic Equilibrium)

Step1: Recall Dynamic Equilibrium

Dynamic equilibrium occurs when an object moves at a constant velocity (acceleration \(a = 0\)). In a velocity - time graph, a constant velocity is represented by a horizontal line (since \(v=\text{constant}\), and \(a=\frac{\Delta v}{\Delta t}=0\) for a horizontal line).

Step2: Analyze Each Time Interval

• 0 to 10 seconds: The velocity - time graph is horizontal (velocity \(v = 10\space m/s\) is constant). So, acceleration \(a = 0\), and the object is in dynamic equilibrium.
• 10 to 20 seconds: The velocity - time graph is a sloped line (velocity is increasing). So, \(\Delta v

eq0\), and \(a=\frac{\Delta v}{\Delta t}
eq0\). The object is not in dynamic equilibrium.

• 20 to 30 seconds: The velocity - time graph is horizontal (velocity \(v = 18\space m/s\) (approx, from graph) is constant). So, acceleration \(a = 0\), and the object is in dynamic equilibrium.
• 30 to 40 seconds: The velocity - time graph is a sloped line (velocity is decreasing). So, \(\Delta v

eq0\), and \(a=\frac{\Delta v}{\Delta t}
eq0\). The object is not in dynamic equilibrium.

Step1: Interpret Velocity Sign

Velocity is a vector quantity. A negative velocity (in the context of horizontal motion) usually indicates motion in the negative direction (e.g., left, if we take right as positive). So, a velocity of \(- 3.0\space m/s\) means the object is moving left.

Step2: Analyze Velocity Magnitude and Change

• The magnitude of the velocity is \(3.0\space m/s\). This means the object's position is changing at a rate of \(3\) meters per second (since \(v=\frac{\Delta x}{\Delta t}\), so \(\Delta x=v\Delta t\), and the rate of change of position is the speed, which is the magnitude of velocity).
• There is no information given about the acceleration, so we cannot say that the velocity is changing by \(3\) meters every second.

Step3: Evaluate Each Option

• "the object is moving left": Correct, due to the negative velocity.
• "the object is moving right": Incorrect, negative velocity implies motion in the opposite (left) direction.
• "the velocity is changing by 3 meters every second": Incorrect, no information about acceleration (change in velocity) is given.
• "the position is changing by 3 meters every second": Correct, since speed (magnitude of velocity) is \(3\space m/s\), so position changes by \(3\) meters per second.

Answer:

0 to 10 seconds, 20 to 30 seconds

Second Question (Velocity of - 3.0 m/s)