Question

13.) write everything you know from the velocity vs. time graph below: (9 required, more are extra credit!)

Explanation:

Step1: Analyze Part A

The object starts from rest (velocity = 0 at t = 0) and has a positive - constant acceleration as velocity is increasing linearly from 0 to 2 from t = 0 to t = 2.

Step2: Analyze Part B

The object has a constant velocity of 2 from t = 2 to t = 3 as the velocity - time graph is a horizontal line.

Step3: Analyze Part C

The object has a negative acceleration as the velocity is decreasing linearly from 2 to 0 from t = 3 to t = 4.

Step4: Analyze Part D

The object has a negative - constant acceleration as the velocity is decreasing linearly from 0 to - 1 from t = 4 to t = 5.

Step5: Analyze Part E

The object has a constant negative velocity of - 1 from t = 5 to t = 7 as the velocity - time graph is a horizontal line.

Step6: Analyze Part F

The object has a positive acceleration as the velocity is increasing linearly from - 1 to 0 from t = 7 to t = 8.

Step7: Analyze Part G

The object has a constant velocity of 0 from t = 8 to t = 9 as the velocity - time graph is a horizontal line at velocity = 0.

Step8: Total displacement in Part A

Displacement $d_A=\frac{1}{2}(2)(2) = 2$ (using the formula for the area of a triangle $A=\frac{1}{2}bh$, where base $b = 2$ and height $h = 2$).

Step9: Total displacement in Part B

Displacement $d_B=(2)(1)=2$ (using the formula for the area of a rectangle $A = bh$, where $b = 1$ and $h = 2$).

Step10: Total displacement in Part C

Displacement $d_C=\frac{1}{2}(1)(2)=1$ (area of a triangle with $b = 1$ and $h = 2$).

Step11: Total displacement in Part D

Displacement $d_D=\frac{1}{2}(1)( - 1)=-\frac{1}{2}$ (area of a triangle with $b = 1$ and $h=-1$).

Step12: Total displacement in Part E

Displacement $d_E=( - 1)(2)=-2$ (area of a rectangle with $b = 2$ and $h=-1$).

Step13: Total displacement in Part F

Displacement $d_F=\frac{1}{2}(1)(1)=\frac{1}{2}$ (area of a triangle with $b = 1$ and $h = 1$).

Step14: Total displacement in Part G

Displacement $d_G=(0)(1)=0$ (area of a rectangle with $b = 1$ and $h = 0$).

Step15: Net displacement

Net displacement $d=d_A + d_B + d_C + d_D + d_E + d_F + d_G=2 + 2+1-\frac{1}{2}-2+\frac{1}{2}+0 = 3$.

Step16: Total distance traveled

Total distance $s=\vert d_A\vert+\vert d_B\vert+\vert d_C\vert+\vert d_D\vert+\vert d_E\vert+\vert d_F\vert+\vert d_G\vert=2 + 2+1+\frac{1}{2}+2+\frac{1}{2}+0 = 8$.

Step17: Average velocity

Average velocity $v_{avg}=\frac{d}{t_{total}}=\frac{3}{9}=\frac{1}{3}$ (where $t_{total}=9$).

Answer:

1. In Part A, the object has a positive constant acceleration and its velocity increases from 0 to 2 in 2 seconds.
2. In Part B, the object has a constant velocity of 2 for 1 second.
3. In Part C, the object has a negative acceleration and its velocity decreases from 2 to 0 in 1 second.
4. In Part D, the object has a negative - constant acceleration and its velocity decreases from 0 to - 1 in 1 second.
5. In Part E, the object has a constant negative velocity of - 1 for 2 seconds.
6. In Part F, the object has a positive acceleration and its velocity increases from - 1 to 0 in 1 second.
7. In Part G, the object has a constant velocity of 0 for 1 second.
8. The displacement in Part A is 2.
9. The displacement in Part B is 2.
10. The displacement in Part C is 1.
11. The displacement in Part D is $-\frac{1}{2}$.
12. The displacement in Part E is - 2.
13. The displacement in Part F is $\frac{1}{2}$.
14. The displacement in Part G is 0.
15. The net displacement of the object from t = 0 to t = 9 is 3.
16. The total distance traveled by the object from t = 0 to t = 9 is 8.
17. The average velocity of the object from t = 0 to t = 9 is $\frac{1}{3}$.