Physics worksheet focusing on displacement, velocity, and acceleration with real-world scenarios.

Here are the step-by-step solutions for each problem on the worksheet.

1. Average Velocity
* Step 1: Identify the distance and time. Distance = $2.0 \text{ km}$, Time = $34 \text{ minutes}$.
* Step 2: Convert units to be consistent (meters and seconds).
* $2.0 \text{ km} = 2000 \text{ meters}$.
* $34 \text{ minutes} = 34 \times 60 = 2040 \text{ seconds}$.
* Step 3: Use the formula: $\text{Velocity} = \frac{\text{Distance}}{\text{Time}}$.
* Step 4: Calculate: $\frac{2000}{2040} \approx 0.98 \text{ m/s}$.

2. Displacement
* Step 1: Identify velocity and time. Velocity = $1.2 \text{ m/s}$ North, Time = $9.5 \text{ minutes}$.
* Step 2: Convert time to seconds. $9.5 \times 60 = 570 \text{ seconds}$.
* Step 3: Use the formula: $\text{Displacement} = \text{Velocity} \times \text{Time}$.
* Step 4: Calculate: $1.2 \times 570 = 684 \text{ meters}$.
* Step 5: Include direction. The answer is $684 \text{ m}$ North.

3. Time
* Step 1: Identify distance and velocity. Distance = $500 \text{ m}$, Velocity = $24.0 \text{ m/s}$.
* Step 2: Rearrange the velocity formula to solve for time: $\text{Time} = \frac{\text{Distance}}{\text{Velocity}}$.
* Step 3: Calculate: $\frac{500}{24.0} \approx 20.83 \text{ seconds}$.

4. Time (Acceleration)
* Step 1: Identify variables. Initial velocity ($v_i$) = $24.56 \text{ m/s}$, Final velocity ($v_f$) = $26.81 \text{ m/s}$, Acceleration ($a$) = $2.80 \text{ m/s}^2$.
* Step 2: Find the change in velocity ($\Delta v$): $26.81 - 24.56 = 2.25 \text{ m/s}$.
* Step 3: Use the formula: $\text{Time} = \frac{\text{Change in Velocity}}{\text{Acceleration}}$.
* Step 4: Calculate: $\frac{2.25}{2.80} \approx 0.80 \text{ seconds}$.

5. Acceleration
* Step 1: Identify variables. Initial velocity ($v_i$) = $-1.3 \text{ m/s}$, Final velocity ($v_f$) = $-4.5 \text{ m/s}$, Time ($t$) = $25 \text{ minutes}$.
* Step 2: Convert time to seconds. $25 \times 60 = 1500 \text{ seconds}$.
* Step 3: Find the change in velocity ($\Delta v$): $-4.5 - (-1.3) = -3.2 \text{ m/s}$.
* Step 4: Use the formula: $\text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}}$.
* Step 5: Calculate: $\frac{-3.2}{1500} \approx -0.0021 \text{ m/s}^2$ (or $-2.1 \times 10^{-3} \text{ m/s}^2$).

6. Final Velocity
* Step 1: Identify variables. Initial velocity ($v_i$) = $-3.00 \text{ m/s}$, Acceleration ($a$) = $-1.4 \text{ m/s}^2$, Time ($t$) = $7.2 \text{ seconds}$.
* Step 2: Use the formula: $v_f = v_i + (a \times t)$.
* Step 3: Calculate the change: $-1.4 \times 7.2 = -10.08 \text{ m/s}$.
* Step 4: Add to initial velocity: $-3.00 + (-10.08) = -13.08 \text{ m/s}$.

7. Deceleration
* Step 1: Identify variables. Initial velocity ($v_i$) = $4.1 \text{ m/s}$, Final velocity ($v_f$) = $0.0 \text{ m/s}$ (stops), Time ($t$) = $2.0 \text{ s}$.
* Step 2: Find the change in velocity: $0.0 - 4.1 = -4.1 \text{ m/s}$.
* Step 3: Use the formula: $\text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}}$.
* Step 4: Calculate: $\frac{-4.1}{2.0} = -2.05 \text{ m/s}^2$.

8. Acceleration
* Step 1: Identify variables. Initial velocity ($v_i$) = $0 \text{ m/s}$ (from rest), Final velocity ($v_f$) = $12.5 \text{ m/s}$, Time ($t$) = $2.5 \text{ s}$.
* Step 2: Find the change in velocity: $12.5 - 0 = 12.5 \text{ m/s}$.
* Step 3: Use the formula: $\text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}}$.
* Step 4: Calculate: $\frac{12.5}{2.5} = 5.0 \text{ m/s}^2$.

Final Answer:
1. 0.98 m/s
2. 684 m North
3. 20.8 s
4. 0.80 s
5. -0.0021 m/s²
6. -13.1 m/s
7. -2.05 m/s²
8. 5.0 m/s²