Final answer:
The motorist's southward movement displacement is 7200 m, westward movement with acceleration is 2460 m, and northwest deceleration until stop displacement is 1581.5 m. Combining these, the total movement of the rider is 11241.5 m. However, since this is not among the provided options, there's an issue with the question or the choices. Calculating the average speed correctly isn't feasible based on this discrepancy.
Step-by-step explanation:
To calculate the movement of the rider for the total journey and the average speed, we need to analyse each part of the trip separately and combine the results.
Southward Movement
First, the motorist travels south at 30 m/s for 4 minutes. Since velocity is constant, the displacement can be calculated as:
Displacement = velocity × time = 30 m/s × 240 s = 7200 m.
Westward Movement
Next, the motorist turns west and travels at 35 m/s for 1 minute, with an acceleration of 0.2 m/s². Here the initial velocity (u) is 35 m/s, acceleration (a) is 0.2 m/s², and time (t) is 60 seconds.
The final velocity (v) can be calculated using v = u + at = 35 m/s + (0.2 m/s² × 60 s) = 47 m/s.
The displacement for this part is given by the formula:
Displacement = ut + 0.5at² = (35 m/s × 60 s) + 0.5 × 0.2 m/s² × (60 s)² = 2100 m + 360 m = 2460 m.
Northwest Movement
Finally, as the motorist veers northwest, he decelerates at a rate of 0.7 m/s² until coming to a stop. Using the kinematic equation v² = u² + 2a × s, with v = 0 m/s (final velocity), u = 47 m/s (initial velocity), and a = -0.7 m/s² (negative because of deceleration), we can find the displacement (s).
s = (v² - u²) / (2 × a) = (0 - (47 m/s)²) / (2 × -0.7 m/s²) = 1581.5 m
The total displacement for the trip is the sum of these displacements: 7200 m + 2460 m + 1581.5 m = 11241.5 m which is not among the options provided, suggesting a possible error in the question or the answer choices.
Average Speed Calculation
The total time of the trip is 4 minutes + 1 minute = 5 minutes (300 seconds).
The average speed is the total displacement divided by the total time. As we calculated an error above for the displacement, the average speed cannot be calculated accurately based on the provided options.