1) Segments A and C
2) Segment C
3) 40 m/s
4) 0
Explanation:
The graph is missing: find it in attachment.
1)
Here we want to find which segments show acceleration.
Acceleration is defined as the rate of change of velocity of an object; mathematically:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
where
[tex]\Delta v[/tex] is the change in velocity
[tex]\Delta t[/tex] is the time interval
On a velocity-time graph, an object has acceleration if its velocity, v, changes versus time.
In this problem, we see that this situation occurs in two segments:
- In segment A, where the is a change in velocity ([tex]\Delta v>0[/tex]), so there is an acceleration
- In segment C, where the is also a change in velocity ([tex]\Delta v>0[/tex]), so there is an acceleration
B)
Here we want to find in which segment the object is slowing down.
For an object to slow down, the final velocity must be less than the initial velocity, which means that the change in velocity must be negative:
[tex]\Delta v = v-u <0[/tex]
where
v is the final velocity
u is the initial velocity
For the graph in the problem, we see that:
- For segment A, the final velocity is greater than the initial velocity, so the object is speeding up
- For segment B, the final velocity is equal to the initial velocity, so the object is neither speeding up nor slowing down
- For segment C, the final velocity is less than the initial velocity, so the object is slowing down
So, the segment in which the object is slowing down is segment C.
C)
The velocity of an object is defined as the displacement covered per unit time:
[tex]v=\frac{d}{\Delta t}[/tex]
where
d is the displacement
[tex]\Delta t[/tex] is the time elapsed
On a velocity-time graph, the velocity is represented on the y-axis, while the time is represented on the x-axis.
Therefore, it is possible to read directly the value of the velocity from the y-axis.
For segment B, we see that the velocity is constant, and its value is
[tex]v_B=40 m/s[/tex]
D)
As we stated before, the acceleration of an object is the rate of change of its velocity:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
where
[tex]\Delta v[/tex] is the change in velocity
[tex]\Delta t[/tex] is the time interval
Here we want to find the acceleration for segment B. For this segment, we observe that:
- The velocity does not change, so [tex]\Delta v = 0[/tex]
- The time interval is [tex]\Delta t = 9 s - 4 s = 5 s[/tex]
Therefore, the acceleration in segment B is:
[tex]a_B=\frac{0}{5s}=0[/tex]
