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Math Help - Kinematics

  1. #1
    Junior Member
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    Kinematics

    Stuck on some problems again

    - A car starts from rest and moves in a straight line. After t seconds, its acceleration, a m s^-2 is given by a=(0.2)(18-t). Find the distance travelled in the first 30 s given that the speed of the car at t=30 is 18m/s.

    I tried to integrate a twice to get S but I can't get the answer of 720m.
     s = \int v\ dt = 1.8t^2 - \dfrac{1}{30}t^3 + C
    Am i doing anything wrong or missing out anything?

    - A particle, travelling in a straight line, passes a fixed point O on the line with a speed of 0.5 m/s. The acceleration, a m/s^2 , of the partiicle , t seconds after passing O, is given by a = 1.4-0.6t

    Find the total distance travelled by the particle between t = 0 and t = 10


    For this I have tried to do the same as the above
     s = \int v\ dt = 0.7t^2 - 0.15t^3 + 0.5t + C
    and i figured that S = 0 when t = 0(since t starts increasing after particle passes O) so C = 0.

    Then i found S at t=5(where it comes to inst. rest) to be 1.25m and S at t=10 to be -75m but doing the math it comes nowhere near the answer of 40m.

    I appreciate any inputs
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  2. #2
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by arccos View Post
    Stuck on some problems again

    - A car starts from rest and moves in a straight line. After t seconds, its acceleration, a m s^-2 is given by a=(0.2)(18-t). Find the distance travelled in the first 30 s given that the speed of the car at t=30 is 18m/s.

    I tried to integrate a twice to get S but I can't get the answer of 720m.
     s = \int v\ dt = 1.8t^2 - \dfrac{1}{30}t^3 + C
    Am i doing anything wrong or missing out anything?

    - A particle, travelling in a straight line, passes a fixed point O on the line with a speed of 0.5 m/s. The acceleration, a m/s^2 , of the partiicle , t seconds after passing O, is given by a = 1.4-0.6t

    Find the total distance travelled by the particle between t = 0 and t = 10


    For this I have tried to do the same as the above
     s = \int v\ dt = 0.7t^2 - 0.15t^3 + 0.5t + C
    and i figured that S = 0 when t = 0(since t starts increasing after particle passes O) so C = 0.

    Then i found S at t=5(where it comes to inst. rest) to be 1.25m and S at t=10 to be -75m but doing the math it comes nowhere near the answer of 40m.

    I appreciate any inputs
    For your first problem, you are given the acceleration a as a function of time ie a=-0.2t+3.6. Integrate this twice wrt t to get the distance and sub in 30s. This will give you 720m.
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  3. #3
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    Quote Originally Posted by bugatti79 View Post
    For your first problem, you are given the acceleration a as a function of time ie a=-0.2t+3.6. Integrate this twice wrt t to get the distance and sub in 30s. This will give you 720m.
    Calculation error for the first question. My bad! Any idea how to do the second qn?
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  4. #4
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by arccos View Post
    Stuck on some problems again

    - A car starts from rest and moves in a straight line. After t seconds, its acceleration, a m s^-2 is given by a=(0.2)(18-t). Find the distance travelled in the first 30 s given that the speed of the car at t=30 is 18m/s.

    I tried to integrate a twice to get S but I can't get the answer of 720m.
     s = \int v\ dt = 1.8t^2 - \dfrac{1}{30}t^3 + C
    Am i doing anything wrong or missing out anything?

    - A particle, travelling in a straight line, passes a fixed point O on the line with a speed of 0.5 m/s. The acceleration, a m/s^2 , of the partiicle , t seconds after passing O, is given by a = 1.4-0.6t

    Find the total distance travelled by the particle between t = 0 and t = 10


    For this I have tried to do the same as the above
     s = \int v\ dt = 0.7t^2 - 0.15t^3 + 0.5t + C
    what i got was 0.7t^2-0.1t^3+0.5t+C. please recheck..
    and i figured that S = 0 when t = 0(since t starts increasing after particle passes O) so C = 0.

    Then i found S at t=5(where it comes to inst. rest) to be 1.25m and S at t=10 to be -75m but doing the math it comes nowhere near the answer of 40m.

    I appreciate any inputs
    did this help?
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