Figure 1 Figure 1 shows the speed-time graph for the journey of a car moving in a long queue of traffic on a straight road. At time t=0, the car is at rest at the point A. The car then accelerates uniformly for 5 seconds until it reaches a speed of 5ms^-1 For the next 15 seconds the car travels at a constant speed of 5ms^-1 The car then decelerates uniformly until it comes to rest at the point B. The total journey time is 30 seconds. (a) Find the distance AB. (b) Sketch a distance-time graph for the journey of the car from A to B. __ (3) (3)

## Step1: Analyze the Speed-Time Graph### The graph shows three distinct phases: acceleration, constant speed, and deceleration. We need to calculate the distance covered in each phase.## Step2: Calculate Distance During Acceleration### The car accelerates uniformly from rest to in 5 seconds. The distance covered during acceleration can be found using the formula for the area of a triangle: ## Step3: Calculate Distance During Constant Speed### The car travels at a constant speed of for 15 seconds. The distance covered during this phase is: ## Step4: Calculate Distance During Deceleration### The car decelerates uniformly to rest in the remaining 10 seconds. The distance covered during deceleration can be found using the formula for the area of a triangle: ## Step5: Sum the Distances### The total distance is the sum of the distances covered in each phase: ## Step6: Sketch the Distance-Time Graph### The distance-time graph will have three segments: 1. A curve representing acceleration from to over 5 seconds.2. A straight line representing constant speed from to over the next 15 seconds.3. A curve representing deceleration from to over the final 10 seconds.#