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Mr Brown is driving his car behind a lorry. The front of the car is 25 metres behind the rear of the lorry and that distance has been maintained for some considerable time. The lorry is travelling at a steady 50 miles per hour. An opportunity arises for the car driver to overtake the lorry. There is a blind bend in the road some 200 metres away. Mr Brown accelerates his car and passes the lorry. According to the manufacturer's literature, the car is capable of accelerating steadily from 50 to 70 miles per hour in 5 seconds. The speed limit is 70 miles per hour. The length of the lorry is 12 metres.
If the car driver is not to exceed the speed limit, what is the shortest time between starting the acceleration and reaching a position where the front of his car is 25 metres ahead of the front of the lorry.
During this time, how far has the lorry travelled and how far has the car travelled ?
The overtake was fully completed before the blind bend. What are your comments about the manner of driving of Mr Brown?
Notes:
This is a graphical question. Plot a graph with the vertical axis representing distance travelled in metres and the horizontal axis representing time in seconds.
Plot the position of the front of the car each second starting at the origin (0,0)
Plot the position of the rear of the lorry each second starting at the point (0,25) because the rear of the lorry is initially 25 metres ahead of the car.
Stop the car's acceleration when it reaches 70 miles per hour or 31.29 ms-1 and then continue the plot with the car's distance increasing by a further 31.29 ms-1 every second.
You will find that the two graphs eventually cross over each other. The cross over point occurs when the front of the car reaches the rear of the lorry.
When the two graphs are separated by (25 + 12) = 37 metres, that is the moment when the front of the car is 25 metres ahead of the front of the lorry.
That moment occurs at about 9.5 seconds.
The lorry has moved about (240 - 25) = 215 metres.
The car has moved (25 + 12 + 25 + 215) = 277 metres.
Mr Brown does not complete his overtake before reaching the blind bend.
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