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Let's go through the questions one by one and provide detailed solutions:

### 1. Determining the acceleration of a car:
- **Initial velocity** (\( u \)) = 20.5 m/s
- **Final velocity** (\( v \)) = 50.1 m/s
- **Time** (\( t \)) = 3.47 s

The formula for acceleration (\( a \)) is:
\[
a = \frac{v - u}{t}
\]
\[
a = \frac{50.1 \, \text{m/s} - 20.5 \, \text{m/s}}{3.47 \, \text{s}}
\]

Calculate this value for the acceleration. Then, to find the distance traveled (\( s \)), use:
\[
s = ut + \frac{1}{2}at^2
\]

### 2. Finding the car's average acceleration:
- **Final velocity** = 70 km/h (convert to m/s: \( 70 \times \frac{1000}{3600} = 19.44 \) m/s)
- **Initial velocity** = 0 m/s
- **Time** = 7 seconds

Use the same formula as before:
\[
a = \frac{v - u}{t}
\]

### 3. Finding the pitch speed:
- **Distance** = 85 m
- **Time** = 4 seconds

The formula for speed (\( v \)) is:
\[
v = \frac{d}{t}
\]

### 4. Calculating bullet travel time:
- **Speed** = 850 m/s
- **Distance** = 1 km (1000 m)

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]

### 5. Derrick’s distance and displacement:
- Walks 4 feet, then turns 90 degrees and crawls 6 feet.
  
For distance, sum up the total movement. For displacement, use the Pythagorean theorem to find the straight-line distance.

### 6. Sir Jan's distance and displacement:
He walks 2 meters to the park and returns. 
- **Distance** = 2 + 2 = 4 meters.
- **Displacement** = 0 meters (since he returns to the start).

### 7. Resultant displacement:
- **Vector A**: 2.3 km at 45° South of West
- **Vector B**: 4.8 km North

Use vector addition to determine the resultant displacement. Decompose each vector into components and sum them.

### 8. Graphical vector addition:
- Vectors: A = 7 m (E), B = 8 m (30° S of W), C = 3 m (NE).

Use the head-to-tail method to add these vectors graphically. Determine the magnitude and direction of the resultant vector.

### 9. Bike ride graph:
- Analyze the graph for each question:
  - **a.** Duration of stationary time.
  - **b.** Total distance.
  - **c.** Average speed over the specified time interval.

### 10. Sprinter's velocity-time graph:
- **a.** Acceleration between 0 and 20 seconds (calculate the slope of the velocity graph).
- **b.** Speed at 8 seconds (check the graph value).
- **c.** Constant speed interval (where the graph is horizontal).

Would you like the solutions worked out in detail for each of these problems?

### Related Questions:
1. What is the significance of using vector components when finding the resultant vector?
2. How does the conversion from km/h to m/s affect the calculation of acceleration?
3. Why is displacement sometimes zero even when distance is not?
4. How can you determine whether a force is acting on an object from a velocity-time graph?
5. What does the slope of a distance-time graph represent?

### Tip:
Always convert units to the standard (e.g., m/s for velocity) before performing calculations to ensure consistency and accuracy.

A series of questions involving physics problems such as determining acceleration, displacement, velocity, and distance using basic kinematics and graphical methods.

This page provides detailed solutions to a variety of physics problems including determining acceleration, displacement, and velocity. It covers kinematic formulas, vector addition, and graphical methods suitable for students in Grades 10-12.

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