This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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You're on a roll — here are the solutions for the questions: 22. (a) The graph shows the speed of a car during an interval of 12 seconds. The distance travelled in the first 4 seconds is 40m. (i) Find the maximum speed reached. Step 1: Use the given distance to find the maximum speed. The distance travelled is the area under the speed-time graph. For the first 4 seconds, the graph forms a triangle. Let the maximum speed be V_max (which is the height of the triangle). The base of the triangle is 4 seconds. The area of a triangle is given by (1)/(2) × base × height. 40 m = (1)/(2) × 4 s × V_max 40 = 2 V_max Step 2: Solve for V_max. V_max = (40)/(2) V_max = 20 m/s (ii) Find the average speed for the whole journey. Step 1: Calculate the total distance travelled for the whole journey. The total distance is the total area under the speed-time graph from t=0 to t=12 seconds. This shape is a trapezium, which can be divided into three parts: 1. Triangle (0 to 4 s): Area = 40 m (given). 2. Rectangle (4 to 10 s): Base = (10 - 4) s = 6 s, Height = V_max = 20 m/s. Area = 6 s × 20 m/s = 120 m. 3. Triangle (10 to 12 s): Base = (12 - 10) s = 2 s, Height = V_max = 20 m/s. Area = (1)/(2) × 2 s × 20 m/s = 20 m. Total distance = 40 m + 120 m + 20 m = 180 m. Step 2: Calculate the average speed. Average speed is given by Total distanceTotal time. Total time = 12 seconds. Average speed = 180 m12 s Average speed = 15 m/s 22. (b) Wafwila left Webuye at 8:00 am towards Mumias at an average speed of 90 km/hr. Nekesa also left Webuye at 8:21 am towards Mumias along the same road at an average speed of 97 km/hr. (i) Determine the time Nekesa caught up with Wafwila. Step 1: Set up equations for the distance travelled by Wafwila and Nekesa. Let t be the time in hours that Wafwila has been travelling since 8:00 am. Distance covered by Wafwila (D_W) = Speed × Time = 90t. Nekesa started 21 minutes later. Convert 21 minutes to hours: 21 minutes = (21)/(60) hours = 0.35 hours Nekesa's travel time = (t - 0.35) hours. Distance covered by Nekesa (D_N) = Speed × Time = 97(t - 0.35). Step 2: Equate the distances to find the time t. When Nekesa catches up with Wafwila, their distances from Webuye are equal: D_W = D_N 90t = 97(t - 0.35) 90t = 97t - 97 × 0.35 90t = 97t - 33.95 33.95 = 97t - 90t 33.95 = 7t t = (33.95)/(7) t = 4.85 hours Step 3: Convert the time t into hours and minutes and add to the starting time. t = 4.85 hours = 4 hours and (0.85 × 60) minutes. 0.85 × 60 = 51 minutes. So, Nekesa caught up 4 hours and 51 minutes after 8:00 am. Time = 8:00 am + 4 hours 51 minutes = 12:51 pm (ii) Determine the distance from Webuye when Nekesa caught up with Wafwila. Step 1: Substitute the value of t into either distance equation. Using Wafwila's distance equation: D_W = 90t D_W = 90 × 4.85 D_W = 436.5 km What's next?