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.