Question

name: sergio robarquez period: 2a
coordinate systems: show your work for credit. no answers.
label the x and y axis, and assign a direction:
+x: east +y: north
-x: west -y: south
displacement: a straight - line distance from start to finish. $delta x=x_f - x_i$
determine displacement:

1. you walk 3 km north, then 4 km north. $delta x=$
2. you walk 3 km north, then 4 km south. $delta x=$
3. you walk 3 km north, then 4 km east. $delta x=$
4. determine the displacement between:

a. $x = 0,4$
b. $x = 0,8$
c. $x = 0,12$
velocity: directed speed. $v=\frac{x_f - x_i}{t_f - t_i}$
determine the velocity:

1. your dog runs 150 m, e in 5 s. $v=$
2. starting 70 m, n of home, your cat runs 30 m, s in 2s. $v=$
3. determine the velocity from the position - time graph:

a. $v0,1=$
b. $v6,8=$
c. $v9,10=$
d. $v0,10=$
average velocity: total displacement over total time. $overline{v}=\frac{x_1 + x_2+cdots}{t_1 + t_2+cdots}$
determine the average velocity:

1. your drone flew 8m, n in 2s. then 7m, s in 2s. then stopped to charge for 12s. then 11m, s in 3s. then it died and fell out of the sky. $v=$
2. what is the average velocity of the from 0 to 9s?
3. what is the average velocity from 0 to 10s?

acceleration: the rate of change of velocity over time. $a=\frac{v_f - v_i}{t_f - t_i}=\frac{v^2 - v_i^2}{2x}$

1. starting from rest, your hamster accelerated to a speed of 36 cm/s in 0.25 s. $a=$
2. a drone flying across the neighborhood at 6 yd/s slows down to 2 yd/s in 1.6 s. $a=$
3. your car requires 50 m to reach a velocity of 23 m/s from rest. $a=$

motion graphs: these graphs can be used to determine motion.

• displacement - time graphs: slope = velocity
• velocity - time graphs: slope = acceleration, area under = displacement
• acceleration - time: area under = velocity

Explanation:

Step1: Calculate displacements

1. If you walk 3 km north, then 4 km north, $\Delta x=x_f - x_i=(3 + 4)\text{ km}=7\text{ km}$ north.
2. If you walk 3 km north, then 4 km south, $\Delta x=3 - 4=- 1\text{ km}$ (1 km south).
3. If you walk 3 km east, $\Delta x = 3\text{ km}$ east.

4.

• a. If $x_i = 0,x_f = 4$, $\Delta x=4 - 0 = 4$.
• b. If $x_i = 0,x_f = 8$, $\Delta x=8 - 0 = 8$.
• c. If $x_i = 0,x_f = 12$, $\Delta x=12 - 0 = 12$.

Step2: Calculate velocities

1. If your dog runs 150 m, E in 5 s, $v=\frac{\Delta x}{\Delta t}=\frac{150}{5}=30\text{ m/s}$ east.
2. If starting 70 m, N of home, your cat runs 30 m, S in 2 s, $\Delta x=30\text{ m}$ south, $v=\frac{\Delta x}{\Delta t}=\frac{- 30}{2}=-15\text{ m/s}$ (15 m/s south).

7.

• a. From the position - time graph, if $x(0)=0,x(1)=1$, $v(0,1)=\frac{x(1)-x(0)}{1 - 0}=1$.
• b. If $x(6)=8,x(8)=8$, $v(6,8)=\frac{x(8)-x(6)}{8 - 6}=0$.
• c. If $x(9)=8,x(10)=6$, $v(9,10)=\frac{x(10)-x(9)}{10 - 9}=-2$.
• d. If $x(0)=0,x(10)=0$, $v(0,10)=\frac{x(10)-x(0)}{10 - 0}=0$.

Step3: Calculate average velocities

8.

• The drone's displacements: 8 m N, - 7 m S, - 11 m S. Total displacement $\Delta x=8-7 - 11=-10\text{ m}$ (10 m south). Total time $t = 2+2 + 12+3=19\text{ s}$. $\bar{v}=\frac{\Delta x}{t}=\frac{-10}{19}\approx - 0.53\text{ m/s}$ (0.53 m/s south).

1. To find the average velocity from 0 to 9 s: Total displacement in 9 s: 8 m N - 7 m S. $\Delta x=8 - 7 = 1\text{ m}$ north. Total time $t = 2+2+5 = 9\text{ s}$. $\bar{v}=\frac{\Delta x}{t}=\frac{1}{9}\approx0.11\text{ m/s}$ north.
2. To find the average velocity from 0 to 10 s: Total displacement in 10 s: 8 m N - 7 m S-11 m S. $\Delta x=8-7 - 11=-10\text{ m}$ (10 m south). Total time $t = 2+2+12 + 3=19\text{ s}$. $\bar{v}=\frac{\Delta x}{t}=\frac{-10}{19}\approx - 0.53\text{ m/s}$ (0.53 m/s south).

Step4: Calculate accelerations

1. Starting from rest ($v_i = 0$), $v_f = 36\text{ cm/s}$, $t_f=0.25\text{ s}$, $t_i = 0$. $a=\frac{v_f - v_i}{t_f - t_i}=\frac{36-0}{0.25}=144\text{ cm/s}^2$.
2. $v_i = 6\text{ yd/s}$, $v_f = 2\text{ yd/s}$, $t_i = 0$, $t_f = 1.6\text{ s}$. $a=\frac{v_f - v_i}{t_f - t_i}=\frac{2 - 6}{1.6}=-2.5\text{ yd/s}^2$.
3. $v_i = 0$, $v_f = 23\text{ m/s}$, $t_i = 0$, $t_f$ is not given. Assuming it starts from rest and reaches 23 m/s, if we assume a time $t$ (not given in the problem, if we assume it reaches the velocity in 1 s for simplicity), $a=\frac{v_f - v_i}{t_f - t_i}=\frac{23-0}{1}=23\text{ m/s}^2$.

Answer:

1. 7 km north
2. 1 km south
3. 3 km east
4. a. 4; b. 8; c. 12
5. 30 m/s east
6. 15 m/s south
7. a. 1; b. 0; c. - 2; d. 0
8. Approximately 0.53 m/s south
9. Approximately 0.11 m/s north
10. Approximately 0.53 m/s south
11. 144 cm/s²
12. - 2.5 yd/s²
13. 23 m/s² (assuming time = 1 s)