8.Two trams , tram A and tram B, run on parallel straight horizontal tracks . Initially the two trams are at rest in the depot and level with each other. At time t=0 , tram A starts to move. Tram A moves with constant acceleration 2ms^-2 for 5 seconds and then continues to move along the track at constant speed. At time t=20 seconds, tramB starts from rest and moves in the same direction as tram A. Tram B moves with constant acceleration 3ms^-2 for 4 seconds and then continues to move along the track at constant speed. The trams are modelled as particles. (a) Sketch,on the same axes,a speed -time graph for the motion of tramA and a speed-time graph for the motion of tramB from t=0 to the instant when tramB overtakes tram A. (3) At the instant when the two trams are moving with the same speed, tramA is d metres in front of tramB (b) Find the value of d. (c) Find the distance of the trams from the depot at the instant when tramB overtake tram A (5)

Let's correct and refine the calculations step-by-step.### (a) Speed-Time Graphs1. **Tram A:** - Accelerates at for 5 seconds. - Speed at : . - Moves at constant speed of after 5 seconds.2. **Tram B:** - Accelerates at for 4 seconds. - Speed at : . - Moves at constant speed of after 4 seconds.### (b) Distance CalculationTo find the distance when the trams are moving at the same speed:- Tram A reaches at .- Tram B reaches at , but it starts 20 seconds later.At , Tram A's speed is and Tram B's speed is .Distance traveled by Tram A in 20 seconds: Distance traveled by Tram B in 4 seconds: Distance traveled by Tram B in the remaining time (16 seconds): Total distance traveled by Tram B: Distance when they are at the same speed: This indicates that Tram B overtakes Tram A before . We need to find the exact time when their speeds are equal.### (c) Finding the Overtake TimeSet the speeds equal: At , Tram B has been moving for (since it started at ).Distance traveled by Tram B: Distance traveled by Tram A: Distance when Tram B overtakes Tram A: ### Summary(a) The speed-time graphs for Tram A and Tram B will show Tram A accelerating to in 5 seconds and then moving at constant speed, while Tram B accelerates to in 4 seconds and then moves at constant speed.(b) The distance when Tram A is in front of Tram B is .(c) The distance of the trams from the depot when Tram B overtakes Tram A is for Tram B and for Tram A.