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Math Help - Finding the distance travelled by a bus

  1. #1
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    Finding the distance travelled by a bus

    A bus is driving towards an intersection where the trafic lights suddenly turns amber. The speed of the bus at that moment is 37.2 km/h.

    The light will remain amber for 5 seconds and then will turn red.

    The driver decides to speed up to cross the intersection before it turns red. For the purpose of this problem, assume that the intersection is crossed when the back of the bus just clears the traffic lights. Also assume that the driver keeps accelerating at constant acceleration until the bus clears the lights.

    The speed limit is 60 km/h.

    What is the maximum distance y(in meters) over which the driver can achieve this aim without exceeding the speed limit?

    Can anyone help me? I have tried at s=ut+ .5at^2
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  2. #2
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    Quote Originally Posted by m_i_k_o View Post
    A bus is driving towards an intersection where the trafic lights suddenly turns amber. The speed of the bus at that moment is 37.2 km/h.

    The light will remain amber for 5 seconds and then will turn red.

    The driver decides to speed up to cross the intersection before it turns red. For the purpose of this problem, assume that the intersection is crossed when the back of the bus just clears the traffic lights. Also assume that the driver keeps accelerating at constant acceleration until the bus clears the lights.

    The speed limit is 60 km/h.

    What is the maximum distance y(in meters) over which the driver can achieve this aim without exceeding the speed limit?

    Can anyone help me? I have tried at s=ut+ .5at^2
    It will depend on the acceleration of the bus (how quickly it can get to 60 km/hr) and the length of the bus. Neither of these thnigs are given ....
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  3. #3
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    Unknown values

    I think we assume that by t=5, the bus reaches 60km/hr. I don't think the length of the bus matters. But check looking at this http://www.mech.uq.edu.au/courses/engg1010/q/bus.jpg

    Does this help in being able to solve the problem?
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  4. #4
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    Quote Originally Posted by m_i_k_o View Post
    I think we assume that by t=5, the bus reaches 60km/hr. I don't think the length of the bus matters. But check looking at this http://www.mech.uq.edu.au/courses/engg1010/q/bus.jpg

    Does this help in being able to solve the problem?
    Quote Originally Posted by mr fantastic View Post
    It will depend on the acceleration of the bus (how quickly it can get to 60 km/hr) and the length of the bus. Neither of these thnigs are given ....
    If the bus is longer, the distance y will be longer. So the maximum distance will be limited by the length of the bus. eg. If the bus was 500m long I doubt all of it would get past the lights in 5 seconds. What if the bus was 1km long ...?

    And as I've already said, it will depnd on the acceleration of the bus and that is not given.

    So as far as I can see at the moment, the question cannot be answered with the data you've provided.
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