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Math Help - 3 General Maths Questions (Kinematics)

  1. #1
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    3 General Maths Questions (Kinematics)

    First Question:
    Assume the acceleration due to gravity is -9.8m/s^2 and ignore air resistance. upward motion is POSITIVE direction

    1.a) a stone is projected upwards from O with a speed of 20 m/s find the velocity of the stone after 4 s.

    ok this is fairly easy so a=-9.8 u=20 t=4
    v=u+at so v=20+(-9.8)4 v=-19.2m/s

    the next part says repeat 1.a) for the stone being projected downwards from O with the same speed.

    since its down then the acceleration is positive. so a=9.8 and the initial velocity (u) is negative since its DOWNWARDS from O. so u=-20 and t=4
    v=u+at so v=-20+9.8x4 v=19.2m/s..... however in my book it says that the acceleration is -9.8... and so then u sub that in the formula and u get v=-59.2 m/s. im just not sure why the acceleration is negative when its downwards. Could some1 explain thanks!

    Second Question:
    A body is travelling at 20 m/s when it passes point P and 40m/s when it passes point Q. Find its speed when it is halfway from P to Q. assuming uniform acceleration.
    ok this question i have no idea lol.. i tried some but i got nowhere. if anyone can explain step by step how to do it thanks!

    Third Question:
    A tram decelerates uniformly from a speed of 60km/h to rest in 60 s find the time taken for it to travel half the total distance.
    ok.. ill leave out some steps but through many checks the total distance(x) travelled is 500m so half of that is 250m. acceleration is worked out to be -5/18m/s^2 and initial speed (u) is 50/3 m/s.
    subbing that in the formula --> x=ut+0.5at^2 250=(50/3)t+0.5(-5/18)t^2 and t is worked to be 17.6s or 102.43s but the answer in my book says its 21.96 s. Is it a mistake in the book or did i make a mistake? Thanks.

    Thats all the questions. Thanks for anyone who can help!
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  2. #2
    Senior Member slevvio's Avatar
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    In the second question the acceleration is still negative because you are still treating upward as the positive direction. In other words it means that things start speeding up in the down direction. If the acceleration were positive the object you dropped would start speeding towards the sky!
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  3. #3
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    i thought that negative acceleration just means deacceleration (slowing down). so when something is dropped downwards it will speed up hence positive acceleration.

    Also acceleration due to gravity (ie something falling down a cliff or a building) is +9.8 meaning speeding up. Anything thats propelled upwards from the ground is -9.8 since its slowing up as it reaches its max height. So i still dont get why the acceleration is negative when its meant to be speeding up and not slowing down.
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  4. #4
    Senior Member slevvio's Avatar
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    Negative acceleration doesn't mean deceleration. The minus sign simply denotes the direction that the acceleration occurs in. In the question the acceleration is ALWAYS negative because the object is on Earth and the attraction is directed downwards.
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