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APPLIED MATHS LINEAR MOTION

  • 12-02-2015 11:24pm
    #1
    leavingcerttt
    Registered Users Posts: 2 ✭


    Two cars both travel at 21m/s in the same direction along a straight horizontal road. At an instant the distance between them is 48m. At this time the driver of the rear car decides to overtake the car ahead. The driver accelerates uniformly at 2m/s(2) until reaching a speed of 27m/s and continues at this speed until the car is 48m ahead of the other car.
    (i) calculate the time taken for the overtaking car to be 48m ahead of the other car.
    (ii) how far does the overtaking car travel from being 48m behind until it reaches 48m ahead of the second car?


Comments

  • #2
    gleesonger
    Registered Users Posts: 166 ✭✭gleesonger


    It's been 10 years since i did any applied maths/physics but i assume the trick is to realise that all you care about is relative distance/velocity.

    Set initial speed for the chase car to zero and see how long it takes to accelerate to the distance required (48*2)

    Edit: just saw second part; from the first part you'll be able to work out the time it takes to reach the required distance. Use the equatuion s=ut+.... With u set to initial speed to find s.

    O and beaware that you break the equations into two parts one covering the acceleration phase and one covering the later constant velocity.


  • #3
    DarraghF197
    Registered Users Posts: 1,307 ✭✭✭DarraghF197


    Lol I can't take this problem seriously when a driver decides to overtake a car that is 48m behind him!

    It's always good to draw diagrams, so just start off with a dotted one.

    This is a rough way I'd tackle it, haven't done a question on this in a while:

    Calculate the time for it to reach 27m/s, which is 3s.
    Calculate both distances travelled in this stage, like 63m for car A and whatever you get for car B.

    So at this point, Car A needs to travel s metres. Car B needs to travel s+48+(48+distance travelled in Stage 1 for car A - distance travelled in Stage 1 for car B).
    You have v as 21 for A
    And v is 27 for B

    Then I suppose s=ut+... And simultaneous equations and away you go! And don't forget to add time for stage 1.


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