Question

diagram 2
time (s) position (m)
0 0
1 6
2 12
3 18
4 24
the object is at rest between 0 and 4 seconds
the object moves 6 meters every second
the objects moves 1 meter every 6 seconds
the object is accelerating
velocity is constant
the object is in dynamic equilibrium
the object is in static equilibrium

Explanation:

Step1: Calculate velocity for each time - interval

Velocity $v=\frac{\Delta x}{\Delta t}$. For $t = 0$ to $t = 1$ s, $\Delta x=6 - 0=6$ m and $\Delta t = 1-0 = 1$ s, so $v_1=\frac{6 - 0}{1 - 0}=6$ m/s. For $t = 1$ to $t = 2$ s, $\Delta x=12 - 6 = 6$ m and $\Delta t=2 - 1=1$ s, so $v_2=\frac{12 - 6}{2 - 1}=6$ m/s. For $t = 2$ to $t = 3$ s, $\Delta x=18 - 12 = 6$ m and $\Delta t=3 - 2 = 1$ s, so $v_3=\frac{18 - 12}{3 - 2}=6$ m/s. For $t = 3$ to $t = 4$ s, $\Delta x=24 - 18 = 6$ m and $\Delta t=4 - 3 = 1$ s, so $v_4=\frac{24 - 18}{4 - 3}=6$ m/s.

Step2: Analyze each statement

• The object is not at rest between 0 and 4 seconds since its position is changing.
• Since the velocity calculated for each 1 - second interval is 6 m/s, the object moves 6 meters every second.
• It is not moving 1 meter every 6 seconds.
• Since the velocity is constant ($a=\frac{\Delta v}{\Delta t}$, and $\Delta v = 0$ as $v_1=v_2=v_3=v_4 = 6$ m/s), the object is not accelerating.
• As the velocity is constant, the object has a constant velocity.
• For dynamic equilibrium, the net force on the object is zero and it is in motion with constant velocity, which is possible here. But constant velocity is a more fundamental description from the given data.
• The object is not in static equilibrium as it is in motion.

Answer:

The object moves 6 meters every second
Velocity is constant