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Math Help - Kinematics in 1d question- very hard

  1. #1
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    Kinematics in 1d question- very hard

    Here is the question:

    A cyclist starts from rest and accelerates at 1.6ms^2 for 10 seconds along a straight horizontal road and then continues at a constant speed. A motorist sets off from the same point as the cyclist at the same time and accelerates at a constant rate for 8 seconds, reaching a maximum speed of V ms^1. The car then decelerates at a constant rate until it comes to rest after a further 15 seconds. At the instant when the car comes to rest, it is overtaken by the cycle.

    A) Calculate the greatest speed attained by the cyclist

    B) Sketch a speed-time graph showing the motions of both the cyclist and the motorist

    C) Calculate the total distanceb travelled by the cyclist before overtaking the car.

    D) Calculate the value of V

    **********************************

    That is the question.

    Now, I can do parts A and C.

    A- 16ms^1
    C- 288m

    I can also do half of part B, as I dont know the value of V I cannot draw the car's motion accurately, however I know the general shape!

    I am having a problem with part D- calculating the value of V. I think that it is 25ms^1; however I am unsure

    Would anyone be able to clarify with me how this question is done?

    cheers
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  2. #2
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    Quote Originally Posted by fishkeeper View Post
    Here is the question:

    A cyclist starts from rest and accelerates at 1.6m/s^2 for 10 seconds along a straight horizontal road and then continues at a constant speed. A motorist sets off from the same point as the cyclist at the same time and accelerates at a constant rate for 8 seconds, reaching a maximum speed of V ms^1. The car then decelerates at a constant rate until it comes to rest after a further 15 seconds. At the instant when the car comes to rest, it is overtaken by the cycle.

    A) Calculate the greatest speed attained by the cyclist

    B) Sketch a speed-time graph showing the motions of both the cyclist and the motorist

    C) Calculate the total distanceb travelled by the cyclist before overtaking the car.

    D) Calculate the value of V
    this entire problem can be solved with a velocity/time graph of the cycle and the car.

    the cycle's graph is a trapezoid with lower base = 23 seconds, upper base = 13 seconds, and height v = 16 m/s

    the area of the trapezoid represents the cycle's displacement for the 23 second period.

    \Delta x = \frac{16}{2}(23+13) = 288 m

    the car's velocity graph is a triangle, whose area equals that of the cycle's trapezoid graph. the base of the triangle is 23 seconds and the height is v max.

    \Delta x = \frac{1}{2} v_{max} \cdot 23 = 288

    v_{max} = \frac{2 \cdot 288}{23} \approx 25 m/s (25.0347826...)
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  3. #3
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    Can anyone advise me on sequences, nth terms etc?

    Thankyou

    I forgot I posted this until I saw my email

    I solved this in a different way, and split the car's graph into 2 parts, for acceleration and deceleration.

    I then found out what each graph held in terms of V e.g. 1/2 * V * 8 etc

    then got 11.5v and divided 288 by 11.5 to get 25.04

    thanks for your time though
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