A driver of train travelling at a speed of 15m/s applies brakes and retardsthe train uniformly. The train stops in 5 seconds. Another train B is travelling on aparallel track with a speed of 10m/s. its’ driver applies the brakes and the trainstops in 10 seconds retarding uniformly.(a) Plot speed-time graphs for train A and Train B on the same paper.(b) Calculate graphically which of the trains travelled farther after the brakes wereapplied.
Question
A driver of train travelling at a speed of 15m/s applies brakes and retardsthe train uniformly. The train stops in 5 seconds. Another train B is travelling on aparallel track with a speed of 10m/s. its’ driver applies the brakes and the trainstops in 10 seconds retarding uniformly.(a) Plot speed-time graphs for train A and Train B on the same paper.(b) Calculate graphically which of the trains travelled farther after the brakes wereapplied.
Solution
(a) To plot the speed-time graphs for both trains, you will need to understand that the speed of the trains decreases uniformly. This means the graph will be a straight line sloping downwards.
For Train A:
- Start at point (0,15) because at time 0, the speed is 15m/s.
- After 5 seconds, the speed is 0. So, mark point (5,0).
- Draw a straight line between these two points.
For Train B:
- Start at point (0,10) because at time 0, the speed is 10m/s.
- After 10 seconds, the speed is 0. So, mark point (10,0).
- Draw a straight line between these two points.
(b) To calculate graphically which of the trains travelled farther after the brakes were applied, you need to find the area under the speed-time graph for each train. This is because the area under a speed-time graph gives the distance travelled.
For Train A:
- The graph is a triangle with base 5 seconds and height 15m/s.
- The area of a triangle is 0.5baseheight = 0.5515 = 37.5m.
For Train B:
- The graph is a triangle with base 10 seconds and height 10m/s.
- The area of a triangle is 0.5baseheight = 0.51010 = 50m.
So, Train B travelled farther after the brakes were applied.
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